October 2017

# How to multiply binary numbers

### Description

Continuing the Bits of Binary series, this episode of House of Hacks shows how to multiple binary numbers. Harley shows how binary number multiplication is as easy as 1 x 1 = 1 and 1 x 0 = 0.

This is the fifth in a series dealing with binary numbers. All the videos in this series can be found on the Bits of Binary playlist.

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 on YouTube.

Here’s the most recent video.

For a written transcript, go to How to multiply binary numbers

All music by Kevin MacLeod at http://incompetech.com and under Creative Commons License By Attribution 3.0.
Intro/Exit: Hot Swing

### Transcript

Do you want to multiply binary numbers together?

In this episode of the House of Hacks, we'll look at how easy this operation really is.

Hi Makers, Builders and Do-It-Yourselfers. Harley here.

The playlist up here contains previous episodes where we looked at what binary numbers are, how to count in binary, how to convert between the more familiar decimal base 10 numbers and binary, and how to do addition and subtraction on binary numbers.

In this episode we'll look at multiplying binary numbers together.

Back when we learned how to multiply decimal numbers in school, we had to memorize a table that looked something like this.

If you know this table, you already know everything there is to know about multiplying binary numbers.

The cool thing is multiplication in binary is exactly the same as decimal except you only use these two rows and columns from the table you've already learned.

And the process is exactly the same too.

Let's take a look at a couple examples and then a couple short cuts.

Let's take seven times three.

Just like in decimal, we first multiply the units and write that down under the equal bar.

Since we're multiplying by 1, we just write down the first number.

Then we add a zero placeholder and multiply by the next column.

Since we're again multiplying by 1, we write down the first number again.

And finally we add the two numbers together to get the total.

1 and 0 is 1.

1 and 1 is two, which in binary is one zero, so we write the 0 and carry the 1.

1 plus 1 plus 1 is three represented in binary as one one, so write the 1 and carry the 1.

Again, 1 plus 1 is 10 so write the 0 and carry the 1.

1 and 0 is again 1 so write the 1 and we're done.

Let's double check this by converting the result to decimal.

Remember each column is a power of two and we add the column values that contain a one.

Looking at the values of the columns we have 16 plus 4 plus 1 which is 21.

Let's do another one. Five times five.

Starting with the units, we multiply by the first number times one and write that down.

We put down a zero placeholder for the next column but notice we're now multiplying by zero.

So we ignore that column since zero times anything is zero, and add another placeholder and move to the next column.

We're again multiplying the first number times one and write it down.

One and zero is one.

Zero and zero is zero.

One and one is two, so write down the zero and carry the one.

One and zero is one.

Finally zero and one is one.

Giving us the result 11001.

Again, we can verify this by converting to decimal.

So we have sixteen plus eight plus one giving us 25.

There are two shortcuts we can observe.

First, since we're always multiplying by either zero or one, the numbers we're adding together are always nothing for zero or the first number shifted by the column that contains a one in the second number.

So this is a really mechanical process of just writing down the first number multiple times shifted as needed and then adding the numbers together.

As an example, we'll take this random number and multiply it by this random number.

We write down the first number with the units under the second number where the columns contain ones.

We can add placeholder zeros if it makes it easier to keep track of the columns.

The second shortcut is related to multiplying by powers of two.

Let's go back to decimal for a minute.

You probably know the shortcut for multiplying by a power of ten.

For ten, one hundred, one thousand, and so forth, all we have to do is add the appropriate number of zeros to the number we're multiplying.

Three times ten is thirty.

Three times a hundred is three hundred, and so forth.

Binary has a similar concept except it's related to powers of two: two, four, eight, sixteen and so on.

Every time a zero is added to the end of a number, it's the same thing as multiplying by two.

So if we are multiplying by two, we add one zero.

If we're multiplying by four we add two zeros, and so forth.

And since powers of two in binary look just like powers of ten in decimal, we really don't have to think about it.

All we have to do is add zeros and we're done.

In this episode, we looked at how binary multiplication is using all the same ideas as decimal multiplication we're already familiar with.

We also looked at two easy shortcuts to mechanically handle the multiplication and multiplying by powers of two.

Binary is a common non-decimal numeric base, but really, any number can be used as a base for a number system.

If this is your first time here at House of Hacks: Welcome, I'm glad you're here and I'd love to have you subscribe.

Through these videos I hope to inspire, educate and encourage makers in their creative endeavors.

In spite of this series, usually this involves various physical media like wood, metal, electronics, photographs and other similar materials.

So 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!

# How to replace a dishwasher

### Description

Need to replace a dishwasher? In this episode of House of Hacks, Harley shows how to install a Bosch 500 series dishwasher after first removing the existing dishwasher. Knowing how to remove and replace a dishwasher is useful information for a home owner. It’s not intimidating once you see how easy they are to install under a counter top.

Bosch 500 series dishwashers on Amazon (Associates link)

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 on YouTube.

Here’s the most recent video.

For a written transcript, go to How to replace a dishwasher

All music by Kevin MacLeod at http://incompetech.com and under Creative Commons License By Attribution 3.0.
Intro/Exit: Hot Swing
Incidental: Beach Bum, Guiton Sketch, Happy Alley and Pump Sting

### Transcript

Need to replace an old dishwasher with a new one?

Today at the House of Hacks, we're going to do exactly that!

[Intro]

For the last six months or so, every once in a while we'd come home and the dishwasher would have leaked. It was a random occurrence. It only happened on rare occasions.

It was pretty frustrating to find. I spent quite a bit of time trying to track it down. I actually went so far as to pull the dishwasher out from the cabinet and put it up on 2 x 4s for a week and we ran it that way to try to isolate where it was leaking. And of course, in that time it never leaked and my wife finally got frustrated with having it out in the middle of the kitchen and asked me to put it back.

Last weekend we came home from running errands and found it had leaked again. It had finished shortly before we got home and I thought maybe it was still wet where it had been leaking and so I immediately pulled it out from the cupboard. I couldn't find any leaks. I was able though to trace the water back from where it was wet on the floor and where it wasn't wet on the floor to kind of get the general region and did some more investigation. I pulled a flashlight out and I did find the tell tale signs of leaking water where you have that white, dried, crustiness from dried water that had been leaking and had since dried. And in tracking it down I found a seam in the tub that had some discoloration in it and that was right where the water was coming out on the other side. And so obviously there's rust through in that seam and there's really no repairing that kind of thing from a practical standpoint. I could kind of hack it with some epoxy or silicone gel, but that's just sort of a stop gap measure and eventually I'm going to have to replace the dishwasher. So I decided to go ahead and do that.

To do this project, I think it's going to require three tools. I may be wrong, but thinking through the project, I think there's three things we're going to need. There's a screwdriver that we'll need to disconnect it from the counter top and also, if there's electrical connections that have screws, they're probably going to be Philips. I think that's the only thing we need Philips for.

The water inlet is probably a compression fitting which will use a 5/8ths inch open end wrench. If it's not a compression fitting, it's probably a hose clamp which again will use the screwdriver.

And finally, I believe the drain has a spring clamp that we'll remove with pliers.

I think that's all we need. Three tools.

If any more are required, when I get into it, I'll talk about that in the process of needing them.

The way this model dishwasher is held in is there's two screws on the top that hold it to the counter top and there's a dust panel on the bottom by the floor that needs to come off so we can move it around.

A total of four screws to pull out and then it should just be able to slide right out.

Let's get to it.

[Turn off the water]

[Turn off the power]

[Loosen dust cover]

[Remove screws]

[Double check there's no power]

[Disconnect drain]

[but put down a towel first]

[Disconnect water supply]

[Access electrical]

[Disconnect wires]

[Remove old machine]

So you saw with the old dishwasher, it had a built in junction box in the bottom front corner that the electrical ran into.

The new one has a separate junction box that is supposed to be mounted away from the dishwasher and then it has this cord that has an end that plugs into the dishwasher.

From a mechanical standpoint, this is a lot easier because I can... I'll have to cut off the old knarly ends and get some new wire here, but there are some screw terminals in there that I'll just screw right into. It'll be quick and easy. But I don't have a good place to mount this. The way the cupboards are designed, the closest place to mount this where it's going to be accessible is further away than the length of this cord. And so, it's just going to float around in the back there.

Let's get this hooked up.

[Trim off old wire]

[Strip insulation]

[Affix strain relief]

[Attach wire to terminals]

[Tighten screws]

[Put on cover]

The water hook up has been a little bit more challenging than I expected.

The dishwasher has a 3/4" MPT fitting on the back of it and my plumbing has a 3/8" flex pipe. So it didn't work directly in there obviously. So I had to go buy a fitting specially for this project that is a 3/4" MPT fitting to a 3/8" compression fitting.

I'm going to put this on and first of all I need to cut off the old compression fitting on the piping because it can't be used again.

[Install fitting]

[Connect water supply line]

OK, now we're going to connect the drain.

This comes from the dishwasher and it has a section for either 1/2" or 3/4" drain pipe.

This pipe is 3/4" so we're going to put the hose clamp on the 3/4" section and push this in there until it's good and seated.

And that's I think as far as it's going to go.

It seems like it should go a little bit further... but maybe not.

Now we put the hose clamp on.

And tighten it down.

I must say I really like the old hose clamp where it was a spring clamp.

It was so much more convenient.

[Install the mounting clips]

[Push the dishwasher under the counter]

OK, now we get the joy of leveling it.

It seems to be in there OK.

All the water and drain stuff, electrical seems good.

It's pretty well centered.

Now it just needs to get leveled and needs to get lifted up actually.

I've got probably almost an inch gap here at the top.

But that's what the leveler feet are for.

OK, to turn this, turn the feet on the right and left to level it side to side.

And to level it front to back, there's a screw right here in the middle you turn to get the front and back level.

[Screw in mounting screws]

[Attach dust panel]

OK. Well, I finally got it done and in.

That was a lot more work than I expected.

The last dishwasher that I'd taken out was one I had also installed 10 years ago or so probably. Maybe 12 years ago.

It was really pretty simple. It was just straight forward: take out the old, put in the new and it was done.

This one there was "some assembly required" as they say.

I had to pick up that part from Home Depot.

I had to wire in things, it was just a little bit more involved.

It was just more work.

It took a lot longer than I expected.

And it took more tools than I expected.

So the final tools:

Scissors to open packaging.

Level to level it.

Tube cutter to cut off the old compression fitting that I didn't need.

A couple adjustable wrenches to level it.

A Philips and a straight screwdriver.

Wire cutters to trim up the wiring.

And a box knife to trim the insulation.

And a 5/8ths inch wrench to tighten up the water connection.

And pliers to put in those little clips. The clips on this particular dishwasher you can put either on the top or on the sides so you had to install those. Use pliers to do that.

That was it. All in all, not a tough job. It just took about 4 hours to do, and that included having to film and setup.

So that slowed it down a little bit. Probably a good 3 hours to do this even if I hadn't been filming.

So that's it for this project.

Thanks for joining me on our creative journey.

Until next time, go make something.

Perfection's not required.

Fun is!