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# A Math Lesson: Binary System

Tuesday, July 1st, 2014 by | Filed Under: Computer Terms, I've Always Wanted To Know...

Have you ever noticed that certain numbers pop up over and over again in computers? Numbers like 32, 256, 512, and 1024 are commonplace, but why not just 30, 250, 500, or 1000? Why is it a 32 GB flash drive instead of a 30?  It is because computers calculate and compute using the binary system.

We have all learned to count using the decimal system. That means we have 10 numerals (deci meaning ten) to use, 0-9. However, computers use a different system called binary. This uses only two numerals – 0 and 1. Everything that a computer processes: words, letters, colors, pictures, is converted to those two numbers through switches on a computer chip. In actuality, to a computer this means “off” (0) or “on” (1). The computer either recognizes a signal or not. This is the reason computers were designed to work with the binary system. We don’t have any way to have a switch “halfway on.”

Unless you are really deep into programming or computer security, you will likely never need any skill in using binary numbers. Once you get into it, though, binary can be kind of fun. However, it does require a different way of thinking, and some simple math skills. I enjoy it because it is a challenge to my brain to think differently.

Here is an example of a binary number:

10011

To figure out the decimal equivalent, let me explain the system a bit.

Similar to the decimal system, binary gets larger as you move to the left. But instead of multiplying by tens for each digit, you multiply by twos. Think about how the decimal system is set up. First you have the ones, then 1X10 is the tens, then 10X10 is the hundreds. Binary is the same, except you have ones, then 1X2 is 2, then 2X2 is 4 and so on. Here is a chart for my example.

 16(8×2) 8(4×2) 4(2×2) 2(1×2) 1 1 0 0 1 1

Remember, if there is a 1, the “switch” is on, and if there is a 0, the “switch” is off. So if there is a one in the box, we add the numbers together. Adding all the ones together you get… (drum roll please)  19! (16+0+0+2+1)

You can extend the digits out as far as you need, each time multiplying the previous number by 2. After 16, you’d have the following values: 32, 64, 128, 256, 512, 1024. These values all pop up over and over in computing, especially in the past when we had smaller values of products like memory cards and flash drives. (When I was in grad school in 2005, I got a 256 MB flash drive to save my work, for free! Wow!)

You can also take a decimal number and convert it to binary. For example let’s start with 55. You would need to look at your binary values (1,2,4,8,16,32,64, etc) and find the largest one that would go into the number. In this case, 32. Place a 1 in that value. Then find the difference between the numbers, which is 23. Then repeat the process, placing a “1” in the place of each value, until you get to 0. I.E. 23-16=7, (do not need 8, so put a 0 in that value), 7-4=3, 3-2=1

110111

There you have it, an introduction to the binary system. And now maybe you will better understand the geeky saying “There are only 10 types of people in the world: Those who understand binary and those who don’t.”

– Audra

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### 5 Responses to “A Math Lesson: Binary System”

1. Barbara Pickett says:

Wow…whether my need to know appetite…and tempting me to get my toes wet…but alas I will probably never do it due to time constraints and old age…LOL keep up the good work.

2. Barbara Pickett says:

…duh.Ms Kindle choosing my words for me…you know I meant whetted don’t you???

• cynthia says:

My Kindle does the same thing. I have to watch her.

3. MarkJ says:

I used to teach an introduction to computers class at our local community college. I assumed that everyone in there was like me and had been taught the idea of different numbers systems in school. I mean like middle school or at least high school but no they had no idea what I was talking about when I said decimal number system, octal, hexadecimal, duo-decimal etc. The concept just wasn’t there at all.

So I attempted to teach them the same stuff you just went through. When I turned around I had a class full of blank stares. All of them still had no idea what was going on.

I never tried to teach binary again.

• James says:

I just have to ask, did you try teaching them the ‘Dewey Decimal System’? Maybe library’s are just not ‘kool’, do kids still say that? Thanks for listening. James

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