Having trouble getting consistent measurements in the workshop? In this episode, Harley gives seven woodworking measuring tips to improve your projects' success.
Here at House of Hacks we do tutorials, project overviews, tool reviews and more related to making things around the home and shop. Generally this involves wood and metal working, electronics, photography and other similar things. If this sounds interesting to you, you may subscribe here.
Music under Creative Commons License By Attribution 4.0 by Kevin MacLeod at http://incompetech.com.
Intro/Exit: "Hot Swing"
Transcript
Are you having problems with consistent measurements on your projects?
Today, I have 7 woodworking measuring tips here at the House of Hacks.
If we're just meeting, I'm Harley and I believe everyone has a God-given creative spark.
Creativity involves connecting the dots in new ways.
The more dots you have, the more creative you can be.
Here at the House of Hacks, I try to show new connections and give you new dots for your own inspiration.
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The first tip is to square the ends that you're going to be measuring from.
This way, if there's any angle, it won't impact the final measurement.
Tip two is to use the same tape measure for your whole project.
This will eliminate any variation from one tape measure to the next, particularly on the ends that move.
Those holes may be slightly different from one tape to the next.
Tip number three is to use a sharp pencil.
This will help minimize any error from the mark itself, both when making the mark and also when lining it up for the cut.
And stay tuned to the end because there's actually a bonus tip at the end.
Tip number four is to use a "V" to mark your cut location rather than a straight line.
This will help reduce the amount of interpretation when lining up to make the cut.
Tip number five is to make one measurement, cut it, make your next measurement, cut it, and so forth.
This will eliminate any drift from the kerf width of the blade.
Tip number six is, if you're making multiple cuts that are the same length, use a stop block.
This way you only have to measure once, it speeds up your production and it also gives you much better consistency.
Tip number seven is to be consistent where you line up the mark with your blade.
The more variance you have in your alignment, the more variation you're going to have in your final product.
And bonus tip number eight is, if you're cutting multiple pieces that are the same length, in addition to using a stop block, if you make multiple cuts at the same time, that'll further reduce the room for error.
Thanks for joining me on this creative journey that we're on.
I'll see you in one of these videos over here that YouTube thinks you'll enjoy.
A contact recently asked "How do I select a power supply for my project?" Once a project moves past the prototyping state using a battery, picking the power supply is a critical element of a personal electronics project. In this episode of House of Hacks, Harley discusses the four items to consider when choosing a surplus power supply.
What do turkey basters and power supplies have to do with each other? And why am I in the kitchen? We're going to talk about all this today at the House of Hacks.
[Music]
Hi Makers, Builders and Do-it-yourselfers. Harley here.
I was recently asked about selecting a power supply for a hacked together project. There are four things when selecting a power supply that you need to pay attention to.
The first two are simple. The last two are a little be more complex but not too bad.
First is the input, you need to make sure that your power supply is appropriate for what you're plugging it into. For the most part you're going to be using locally supplied power supplies, probably surplus stuff that you've scavenged, and in that case it's going to work because it's designed for your local environment. In the United States that's going to be 110 to 120 volts AC. Pretty much anywhere else in the world, with a few exceptions, it's 220-240 volts AC. So the first item, while it's there and you need to be aware of it, it's really simple.
The second item has to do with the output. Power supplies can either output volts AC, indicated by VAC or a squiggly line or it can output in volts DC, indicated by VDC or a straight line. And you need to select the type of current that's appropriate for your project. Most, if you're doing low-voltage stuff, most of those are going to be DC, but depending on what you're working on, AC may be appropriate for your case.
The last two items are volts and amps. And these are similar to properties of water systems so we'll look at that here in a minute with the turkey baster and the sink.
But in short, volts have to do with, kind of, the pressure that the electrons are pushing into your circuit. And you need to make sure that this is appropriately ranged for your circuit you're working with. Generally circuits have a minimum and maximum voltage. You need to make sure that the voltage coming from the power supply fits within those parameters.
And finally there's amperage. Amperage is more like capacity. So it has to do with, as long as your power supply meets minimum requirements for your circuit, you're good to go. Your power supply can provide more amps than you need, it just can't provide less. So, make sure you know what your circuit requires and your power supply at least meets that minimum.
For example, a circuit that requires 250 milliamps (ma) would work just fine with a power supply that supplies 250 ma, 500 ma or 100 amps. Any of those would work just fine. However, if the power supply says it's rated for 100 ma, that's going to be too little and your circuit won't work right.
So let's go look at the sink and see how water correlates to volts and amps.
OK. As I mentioned, volts have to do with the amount of pressure and amps have to do with the capacity.
If you think about a water system, there's a whole lot of capacity here. The city has probably thousands of acre-feet of water that are sitting behind these pipes. They can provide pretty much all the capacity that we need for our little simple demonstration here.
It also has a lot of pressure. We control the pressure by the knob here, the lever, and if we put this on here and we give it just a little bit. This would be like not enough volts where we have a really weak stream here and the circuit isn't going to work right because it just doesn't have enough oomph to make it work.
If we increase the pressure to just the right amount, we get a nice flow without overdoing things and we reach a point of equilibrium here where the equivalent of the circuit is going to work just fine because we have the right amount coming in, not too much, not too little and everything's going to work just fine. And this is kind of equivalent to the volts controlled by the lever here.
If we increase the voltage too much though, what we end up with is a lot of leaks. And when you have leakage in electronics, that's a really bad thing. Things tend to blow up, burn up, magic smoke escapes, all that kind of good stuff. So you really don't want to put too much voltage to your circuit. You want to have just the right amount of volts that you get a good flow like that without having too much.
But now in all these cases, regardless of how much voltage I had, how much pressure I had coming out of the circuit, I still had huge, huge, vast amounts of water sitting in reservoirs behind these pipes. And that's equivalent to your amps. Your circuit will only use the amount of amps that it needs, regardless of how much capacity your power supply has.
So in summary, there are four things to look at: the input voltage and current and the output current, volts and amps. Make sure that you have the sufficient volts within the range that the circuit is designed for and that you have at least the minimum number of amps that are required by the circuit and you're good to go.
A pair of momentary switches become a latching on/off switch as Harley expands on a previous video about remote controlling a shop vac. This is the first of several in a modular switching system to remote control shop equipment using the PowerSwitch Tail II.
The central part of this system is the PowerSwitch Tail. It contains an electronically controlled switch to turn things on an off. There are a large number of ways to control this. In this episode, we introduce a modular system to allow different types of switches to be used to control the shop vac (or any other type of appliance).
Music under Creative Commons License By Attribution 3.0.
Intro/Exit: "Hot Swing" by Kevin MacLeod at http://incompetech.com
Special effects: livingroom_light_switch by AlienXXX at http://freesound.com
Transcript
Last year I showed an easy way to remote control shop equipment using a PowerSwitch Tail, a couple batteries, a switch and some wire.
Today at the House of Hacks I’m going to show how I made a push-on/push-off switch that mimics the way a lot of shop equipment are controlled.
[Music]
Hi Makers, Builders and Do-it-yourselfers. Harley here.
Just a quick reminder, if you haven’t done so already, subscribe to the House of Hacks channel to get notified of future videos.
Last year I made a video responding to a comment by Rob about how I made the remote control switch on my central shop vac system.
In that video, I showed the core design element: the PowerSwitch Tail and how to use it with a simple battery operated switch.
Today i’m going to show a different way to control the same PowerSwitch Tail by eliminating the batteries and using a switch with two buttons: one to turn the tool on and one to turn it off.
This is similar to how many shop tools are controlled. It also has the additional feature of being able to be expanded upon in the future.
If you recall, the PowerSwitch Tail requires 3 to 12 volts DC applied to these two connectors to cause the tool to turn on.
Batteries are of course one source of power for this but they need to be replaced on occasion.
Since I didn’t want to deal with replacing batteries, in my application I decided to use a surplus wall wart style power supply. I had a bunch of these lying around and figured this would be a good application for one of them.
I plugged it into the same outlet I plug the PowerSwitch Tail into.
I connect the low voltage power supply to two connectors on an RJ-11 jack.
Then I connect the other two connectors on the RJ-11 jack to the two connectors on the PowerSwitch Tail.
This allows me to use a phone wire as an extension cord.
For the switch's end, I put another RJ-11 jack in a project box. This project box can now have any type of switch mechanism in it I want and provides a nice modular way to use different types of switches.
For example, I could put in a toggle switch just like I showed in the last video.
Simply wire the negative side of the power to the negative input on the PowerSwitch Tail and wire a switch between the positive side of the power and the positive input for the PowerSwitch Tail.
However, since we have power in the project box, we aren’t limited to just a simple mechanical switch.
We can build circuitry that controls the PowerSwitch Tail.
The first thing I’ve made is a simple latching switch.
Similar to the switches on many tools, like my drill press and my bandsaw, I press the green button to turn on my vacuum and push the red button to turn it off.
Inside the box is a simple flip flop.
A flip flop is a type of circuit with two inputs, called Set and Reset. It also has two outputs, called Q and bar Q, or also known as not Q. It’s just the inverse of Q.
The inputs receive momentary pulses.
If the pulse is on Set, then Q goes high and bar Q goes low.
If the pulse is on Reset, then Q goes low and bar Q goes high.
If we consider just one output, Q, we can see Set causes it to turn on and Reset causes it to turn off. It just flip flops between the two positions.
Flip flops can be made with a variety of different circuits ranging from discrete components to various types of integrated circuits.
I happened to have a Quad 2-Input NOR gate chip in my parts bin so I used that.
But I could just as easily have used NAND gates, a chip with a dedicated flip-flop circuit in it, or a couple of transistors and resistors.
Once I had the circuit built, all I had to do was put it in the box and wire it up.
The switches are wired with pull down resistors. This allows the inputs to be normally low and go high when the button is pressed.
The green button connects to the Set input. The red button connects to the Reset input.
The negative input to the PowerTail Switch goes to the negative power connector.
Since I’m switching the positive side of the power, I’m using a PNP transistor.
Its base connects to the flip-flops Q output.
The PowerSwitch Tail’s positive input goes to the transistor’s collector.
And finally, the transistor’s emitter connects to the positive power connector.
In this configuration, the transistor acts as the switch for the PowerSwitch Tail’s power.
When it’s all put together, pushing the green button turns on the appliance and pushing the red button turns it off.
Since this switch system is modular, I have plans to build other switches too.
The next one is a current sensing switch so the vacuum will automatically turn on when a tool is in use and will turn off, after a short time delay, when the tool is turned off.
I’d love to know in the comments below if the level of detail I presented here was too much, just right or too little.
If this is your first time here at House of Hacks: Welcome, I’m glad you’re here and would love to have you subscribe.
I believe everyone has a God-given creative spark.
Sometimes this manifests through making things with a technical or mechanical bent.
Through this channel I hope to inspire, educate and encourage these types of makers in their creative endeavors.
Usually this involves various physical media like wood, metal, photography, electronics, like in this video, and other similar materials.
If this sounds interesting to you, go ahead and subscribe and I’ll see you again in the next video.
Thanks for joining me on our creative journey.
Now, go make something. Perfection’s not required. Fun is!
Histograms can be found in Photoshop for use in post-processing, not only on the back of our cameras when making the exposure. In this final episode of the Histogram series, Harley shows the different places histograms show up and what they represent within the image.
Music under Creative Commons License By Attribution 3.0.
Intro/Exit: "Hot Swing"
by Kevin MacLeod at Incompetech
Sound effect: living-room-light-switch by alienxxx at FreeSound
Transcript
Histograms are an important tool when making an image in-camera. They also have their use during post-processing. In this episode of House of Hacks, I talk about how they work in Adobe’s Photoshop.
Hi Makers, Builders and Photographers. Harley here.
This is one in a series of videos about understanding and using the histogram. The others can be found in this playlist. I also have a playlist of other topics related to photography.
Today, we'll look at histograms in Photoshop. In this application, histograms tell us the same information as they do on the back of the camera but instead of just one histogram, Photoshop has several because of the different ways to view the image.
First off, if the histogram isn't visible, go to the Windows menu and select Histogram or you can click this icon.
By default it shows a little view like this. Click on this option drop down and select "All channels view" to see multiple histograms, one for each channel.
In many images all the channels will be very similar. But in some instances they might be quite different.
The split channels can be useful in situations where one color is predominant in your image. They help you see how adjustments to the image impact each color to help you know when one channel might start clipping, losing detail in the final image.
There's also this combo box that controls what is displayed in the top histogram. Personally, I like to show luminosity.
These histograms show the information for the image with all the adjustment layers applied. It’s the final histogram for the processed image.
As you turn adjustments on and off, you can see the histograms change accordingly.
Histograms also show up in some adjustment layers such as levels and curves.
The histograms that show in adjustments are the histogram for the image as that layer sees it, taking into consideration the original image and any layers below the current layer. This means adjustment layers above and below the current layer may have different histograms than the current layer.
As an example, this levels adjustment layer has a histogram for the original image.
If we make some adjustments and then add a curves adjustment above it, the curves layer shows a histogram based on the changes made by the levels adjustments.
If we make some adjustments on the curves layer, we can see the main histogram shows the results.
Also, if we make adjustments in a particular color channel, we can see how those changes impact that channel in the global histogram view.
If our adjustments are too extreme, we can see in the channel’s histogram that we start to lose details in this particular channel without the typical clipping showing in the main histogram curve.
In conclusion, I’d love to hear in the comments below about your experiences with the histogram, particularly during post-processing.
If this is your first time here at House of Hacks: Welcome. I’m glad you’re here. We’d love to have you subscribe. Through this channel I hope to inspire, educate and inform makers in their creative endeavors. Usually this involves various physical media like wood, metal, electronics, photographs and other similar materials. Thanks for joining me on our creative journey. So subscribe and I’ll see you again in the next video.
Now, go make something. It doesn’t have to be perfect, just have fun!
Subtraction can be done two ways using binary numbers. This episode talks about unsigned subtraction, very similar to how we do it in decimal notation. We'll dive into the details in this episode of Bits of Binary at the House of Hacks.
Music under Creative Commons License By Attribution 3.0.
Intro/Exit: "Hot Swing" by Kevin MacLeod at http://incompetech.com
Transcript
That may look confusing on the surface, but if you saw the last Bits of Binary episode, it might make some sense. I'll explain it in more detail in this episode of the House of Hacks.
Hi Makers, Builders and Do-It-Yourselfers. Harley here.
This is a continuation in the series on Bits of Binary. In previous episodes I explored the concept of binary numbers, how to count in binary, how to convert between binary and decimal and, in the last episode, I showed how to add binary numbers together. In this episode, I'll show the simple, obvious way to subtract them that's analogous to how we first learned it in decimal. In a future episode I plan to introduce the non-intuitive way negative numbers are stored in computers and how that impacts subtracting binary numbers.
Remember last time when we talked about addition, we looked at these two tables...
Let's remember how we use this with decimal numbers. We'll ignore negative numbers for now so we'll establish the rule that the first number has to be larger than the second. Since this half of the table is the same as this half, we’ll just ignore one side.
When describing the process, we'll use the example 8 - 5.
The process is to first find the entries in the table for the first number. Then, of those entries, you find the one with the other number in the header. The answer is the other header value.
Binary is exactly the same way, just with the much smaller table. Or written as a series of equations, it looks like this.
The first three probably make intuitive sense as they are the same as decimal. But the last one may not be quite so obvious. Remember that in binary the value for two is represented by 1, 0.
If we recall from grade school, with multi-column numbers, when we subtract a larger number from a smaller one, we have to borrow from the next higher column. Let's take for example 21 - 13 in decimal. The units column is 1 - 3. Well, we can't do that, so we borrow a one from the 2 in the second column giving us 11 - 3. This gives us 8. Moving to the next column we now have 1 - 1, giving us 0.
Binary works exactly the same way. Let's look at some examples in binary.
First something simple: 6 - 2. The units column is 0 - 0 equals 0. The next column is 1 - 1 equals 0 again. The final column is 1 - 0, giving us 1. This gives us an overall result of 100, or the value 4.
Now let's do something with some borrowing: 6 - 3. The units column is 0 - 1. We can't do that so we're going to borrow a 1 from the next column. Now we have 10 - 1 giving a result of 1. Because of the previous borrow, the second column is 0 - 1. So again we borrow from the next higher column giving us 10 - 1 with a result of 1. The final column is 0 (because of the previous borrow) - 0 giving us 0. Overall, the result is 11, or a value of three.
And that's it. Subtraction is a bit more complicated due to the borrowing, but again, it's a known concept just applied in a slightly different way.
Thanks for watching this episode of Bits of Binary. As I mentioned earlier, a future episode will explain how negative numbers are handled in a computer and a less-intuitive but ultimately easier way to handle subtraction. But in the next episode, I'll look at multiplying binary numbers together.
I've created a playlist over here that will be filled in as more episodes in this series are added.
If you liked this, let me know with a "thumbs up.".
If you have any thoughts or questions on this topic, I'd love to hear them in the comments below.
If you're already a subscriber, "thank you!" and if you haven't done so already, be sure to "subscribe" so you don't miss future on topics such as this one, high-speed photography, making a digital computer with 19th century technology and much more.
Until next time, go make something. It doesn't have to be perfect, just have fun.
Addition is probably one of the most common operations when using binary numbers. And it's really easy to do. We'll see how easy in this episode of Bits of Binary at the House of Hacks.
Music under Creative Commons License By Attribution 3.0.
Intro/Exit: "Hot Swing" by Kevin MacLeod at http://incompetech.com
Incidental: "Zap Beat" by Kevin MacLeod at http://incompetech.com
Transcript
One plus one equals... huh? I'll talk about how this actually makes sense, today at the House of Hacks.
[Introduction]
Hi Makers, Builders and Do-It-Yourselfers. Harley here.
In the last episode of Bits of Binary, I showed how to convert between decimal and binary numbers. In this episode in the series, we'll look at how to add binary numbers together.
Remember in grade school when you had to memorize this addition chart?
Well, OK, maybe you didn't have to memorize it, but I sure did.
This table is a matrix with the 10 numbers found in the decimal system, 0 through 9, on both the row and column headers. Each cell contains the sum of its row and column header. This gives us the sums for all the single digit combinations. 0+0=0 all the way up to 9+9=18. Multi-digit numbers can be added by simply thinking of them as multiple single digit combinations.
Well, binary has something similar, but much, much smaller. Since there are only two numbers in the binary system, 0 and 1, the table only has two rows and two columns. And it looks like this.
Or if you want to write it a slightly different way as equations, it looks like this.
Once you know this table, the process of adding in binary is exactly the same as adding in decimal. For example let's look at the decimal numbers: 321 + 181. Staring with the units: 1+1 = 2, 2+8 = 10 so write 0 and carry a 1, 1 + 3 = 4 + 1 = 5.
Similarly, in binary we'll look at 1011 + 10. Starting with the units on the right: 1 + 0 = 1, 1 + 1 = 10 so write 0 and carry a 1, 1 + 0 = 1, 1 + 0 = 1 again.
That's it. Addition is short and sweet. Thanks for watching this episode of Bits of Binary. In the next episode, we'll look at how to subtract binary numbers.
I've created a playlist over here that will be filled in as new episodes in this series are added.
Thanks to everyone who has subscribed to this channel and liked the videos.
Be sure to leave a comment if you have any thoughts or questions on this topic.
And until next time, go make something. It doesn't have to be perfect, just have fun!
Music under Creative Commons License By Attribution 3.0.
Intro/Exit: "Hot Swing" by Kevin MacLeod at http://incompetech.com
Transcript
If you don't get this classic joke, by the end of this episode you should. Today I explain how to convert binary to decimal, and back again, here at the House of Hacks.
Hi Makers, Builders and Do-It-Yourselfers. Harley here.
In the last two episode of Bits of Binary, I introduced alternate number systems in general and the binary system in particular. Next I showed how you can use binary to count much higher than ten on just your fingers. I closed with the question "How high can you count in binary on both hands?" If you came up with the answer 1023, you really understand the basics.
In this episode in the series, I'm going to show how to convert from binary to decimal and from decimal to binary.
Last time, I explained how each column in a number is the base number raised to a power times the value of the column. That sounds more complicated than it is. In our familiar base 10, or decimal, system, the columns are 10^0, 10^1, 10^2 and so forth. This gives us columns that represent units, tens, hundreds and so on. To get a specific number, say 123, you simply multiply the number in the column by the column's value. Or (100 * 1) + (10 * 2) + (1 * 3). Applying this principal to binary, the columns are 2^0, 2^1, 2^2 and so forth. Giving us 1, 2, 4, 8 and on up.
So, let's convert from binary to decimal. What's the decimal value of the number 10101? Given that each column represents a power of two and each column can only have a value of 0 or 1, this means its value is (2^4 * 1) + (2^3 * 0) + (2^2 * 1) + (2^1 * 0) + (2^0 * 1). Removing the items multiplied by zero gives us (2^4 * 1) + (2^2 * 1) + (2^0 * 1). Evaluating the exponents gives us (16 * 1) + (4 * 1) + (1 * 1). And all this simplifies to 16 + 4 + 1 or 21 in decimal.
Now that we know the theory, let's look at some shortcuts. Instead of looking at the columns as 2 to a power, we can look at them with specific values. Starting with the units column, we know it's one. Each subsequent column is the current column times 2. This gives us 1, 1 * 2 is 2, 2 * 2 is 4, 4 * 2 is 8, 8 * 2 is 16 and so on. Next, all we need to do is write the binary number below the numbers: 10101. And then simply add the values of the columns with 1's in them. 16 + 4 + 1 = 21 decimal.
Binary to decimal is really pretty simple.
Next, let's convert from decimal to binary. This is slightly more complicated, but still not hard.
We need to start with a binary column value larger than our decimal number. So, we start at the right side with one and multiply by two until we have a number larger than what we want to convert. Then working from the left we apply this rule: if the value we want to convert is greater than or equal to the column value, then we set a one for that column and subtract the column's value, otherwise, we set a 0 for that column and continue. The result is then applied to the next column. And we apply the rule until we reach zero.
Let's try the earlier example of 21 decimal. First, find the columns. Start with 1 and double until we have a value greater than 21. Then start from the left and apply the rule. 21 is less than 32 so we write a 0 and move to the next column. 21 is greater than 16, so we write a one below the 16 and subtract 16 from 21 leaving us 5. Next column. Five is less than 8 so we write a zero below 8 and move on. Five is greater than 4 so we set a one below the four and subtract four from 5 leaving us 1. One is less than 2 so we set a zero below the 2 and move to the units. One is equal to one so we set a 1 in the units column, subtract 1 from one leaving us zero and we're done.
If we get to the end without reaching zero, we've done something wrong and need to recheck our work.
Looking at the binary value, we have 10101, which is what we saw in the previous example of binary to decimal, so it all works.
Let's try 24 decimal as another example. 24 is greater than 16, so we set a one below the 16, subtract 16 from 24 leaving us 8. 8 is equal to 8 so set a one below the 8 and subtract 8, leaving us 0. Since we know 0 is less than all the other columns, we can just set them to 0 and be done. This leaves us 11000 binary.
That's all there is to convert between binary and decimal.
I've created a playlist over here that contains all the episodes in this series so far and will be filled in as more are added.
Thanks for watching and if you learned something, I'd appreciate a thumbs up If you have any questions or comments, leave them below. I try to respond to all of them.
So until next time, go make something. It doesn't have to be perfect, just have fun!
Music under Creative Commons License By Attribution 3.0.
Intro/Exit: "Hot Swing" by Kevin MacLeod at http://incompetech.com
Incidental: "Feelin Good" and "Cold Funk" by Kevin MacLeod at http://incompetech.com
Transcript
If you recognize this as the number 31, you can skip this video. But if you want to know how to count to 1023 on just your fingers, we'll find out in this episode of the House of Hacks.
Hi Makers, Builders and Do-It-Yourselfers. Harley here.
In the last episode of Bits of Binary, I talked a bit about different binary systems in general and binary numbers in particular. You can click here if you're interested in this introduction.
In this episode, I'll start with the basics of decimal numbers that you may already know. I'll then relate that to alternate number systems in general and then binary numbers specifically. Finally I'll wrap up with how to count in binary.
When we were young, we learned to count on our fingers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
A couple years later we learned there's actually a special value that's no quantity: 0. And and with this new knowledge we found that 10 really isn't a number in the same way as the other nine are. It's a combination of 1 and this new non-value value. We found that at the core, we have 0 through 9 as our ten digits, not 1 to 10.
While were were still reeling from this new information, we learned you can count the groups of 0 through 9 and keep track of that in the "ten's column." So, now we could have 10 through 19 and 20 through 29 all the way up to 90 through 99. And then we could add a "hundreds column" for 100 through 199 and so forth. Numbers could actually be arbitrarily large by just adding another column.
This was mind blowing!
There were numbers incomprehensibly large to our young minds like "million" and "billion" with all kinds of crazy numbers of columns.
Then as we grew and got more sophisticated, we learned about something called exponents. These columns we were so comfortable with could now be represented by 10 raised to number of the column. So the "ten's column" was 10^1 and the "hundred's column" was 10^2. The "unit's column" took advantage of a weird property of exponents that said "anything raised to the power of 0 is 1."
It was explained any number could be split into its constituent parts by taking the digit in each column and multiplying it by the power of 10 for that column and adding the results together for the other columns. We found the simple columns we learned early in our education were just shorthand for much more heady concepts.
For example, the number 123 could be written (1 x 10^2) + (2 x 10^1) + (3 x 10^0).
If you're anything like me, this is about where the educational system stopped. There was no direct talk about this "5" being an abstract symbol for an underlying value. They did talk about it in an oblique way when they talked about other cultures having other number systems such as Roman numerals I, V, X, L and C. But that was about it. It was simply given that "5" meant "*****" this many things.
This was the decimal number system and how those of us now middle aged in the United States probably learned it.
If you had your young mind blown when you learned the ten's column was 10 raised to 1 and the hundred's column was 10 raised to 2, here's another mind blowing revelation...
The column base, the 10 so far, doesn't have to be limited to the number 10. It can be any anything!!
For example, this base could be 16 where you'd have the familiar zero and 15 other symbols. In this base, this many objects "**** **** **** ****" would be written as 10. Even though it looks like ten, it isn't. It's sixteen. And if you add one more "*", it'd be written 11 meaning seventeen.
Or the base could be 8 where you'd have zero and 7 other symbols. In this case the quantity seventeen would be represented by the series of digits 21. But in decimal, it'd still be represented by 17 and in base 16 it'd still be 11.
When dealing with multiple number systems at the same time, typically we put a subscript after the number to indicate the base for that number. So in the example of seventeen items, the previous bases would be written as 11(16), 21(8) and 17(10). This helps reduce confusion. But typically only one system is used at a time, and the base is left off, since it's implied by the context.
As you're trying to get your brain around all this, let's talk specifically about today's topic: binary. Its base is 2 so all we have is zero and one other digit: 1. That's it. 0 and 1, 1 and 0. Easy!
Let's look again at the columns we learned about when we learned about exponents. Just like in decimal where column one was 10 to the 0 and column two was 10 to the 1 and column three was 10 to the 2 and so on, in binary column one is 2 to the 0 and column two is 2 to the 1 and column three is 2 to the 2. That means the value of these columns if we multiply them by 1, are 1, 10 and 100 for decimal. And for binary they are 1, 2, 4, 8 and so forth.
Going back to our earlier example, in decimal, for each column's power of ten, you can multiply it by a number from 0 to 9, because your base is 10.
Binary however is much easier. For each column's power of two, you can only multiply it by either 0 or 1, because that's all the digits we have.
So, let's see what happens when we count from 0 to 10. For comparison, let's see both decimal and binary side by side. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
See this pattern...
If we use a finger to indicate one and apply this pattern to our fingers...
zero, one, two, three, eight, nine, ten.
By continuing this pattern, on one hand we can count to the number 31. This is 16. Plus 8. Plus 4. Plus 2. Plus 1. That totals 31. So, how high can you count using both hands?
Thanks for watching this episode of Bits of Binary. In the next episode, we're going to look at how to convert back and forth between binary and the more familiar decimal numbers.
And I've created a playlist over here that will be filled in as more episodes in this series are added.
If you liked this, let me know by hitting the "like" button.
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I'd love to hear from you in the comments below if you have any thoughts or questions on this topic.
Until next time, go make something. It doesn't have to be perfect, just have fun!
What do Morse Code, Braille and binary numbers have in common? Let's find out today at the House of Hacks.
Hi Makers, Builders and Do-It-Yourselfers. Harley here.
As I think about different videos I want to do in the future, certain areas of knowledge seem to recur. They're somewhat foundational. I plan on doing a couple series on these foundational topics. But don't worry. I'm not going to do them exclusively. I'll intersperse them with my normal projects and other tutorials. This is the first episode in the first of these series. And now, to the topic at hand.
Morse code uses short signals called dits and long signals called dahs in various combinations to encode letters, numbers and other symbols. The dits and the dahs can be represented by long and short sounds, or blinking lights or any other method of indicating two states.
For example, this is the letter "A." And this is the letter "B." And here's "Hello world."
The interesting thing here is there are two things, a dit and a dah, in the context of silence to separate letters and words to communicate.
Braille uses a two by three grid containing various patters of raised to encode letters, numbers and other symbols.
For example, this is the letter "A." And here's the letter "B." And here's "Hello world."
Braille is used predominately to allow blind people to communicate in written form. Interestingly, it was adapted from a similar system used by the French military to communicate on the battlefield without using sound or light that might give away their position to the enemy. So, it doesn't have to be used exclusively by the vision impaired. But that's a bit of a historical side note.
The important thing for the purpose of this discussion is to note it uses either the presence or the absence of a raised dot. A bit of information, in the context of other bits of information, the two by three grid, to convey more information.
Binary number systems use just zero and one to represent numbers.
For example, this means one. And this means two. And this means ten.
Computers use either the presence or absence of a voltage to indicate either zero or one. And they build sequences of these up into numbers to represent symbols, numbers and letters.
So, what is binary?
Simply, binary is defined as something having two parts. Each of these systems we've talked about today use just two things, within a context, to encode information. Morse code uses sequences of dit and dah. Braille uses the absence or the presence of a dot within a grid. And binary numbers use zero and one within a sequence.
In future episodes in this series, I'll be discussing binary numbers in more depth. How to correlate them to the decimal system you're probably already familiar with and how to perform mathematical operations on them.
There's a playlist over here that will have new episodes added to it.
And finally "Thank you" if you've already subscribed. You can configure YouTube to notify you when new episodes are available. If you aren't subscribed and you want to get those notifications, be sure to subscribe. It's free and contains zero calories. Finally, if you're interested in this series, go ahead and hit the "like" button, that'll let me know there's interest in this.
Thanks for watching and until next time, go make something. It doesn't have to be perfect, just have fun.
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