It’s Easy To Count To One

Tuesday, February 20th, 2007

I work with computers for a living. Often when I tell people that, the response is, “I could never do that.” But, like many things, computers only seem confusing. Don’t get me wrong, a modern computer is a pretty amazing culmination of science, technology, invention, and manufacturing, but I’m convinced that anyone can understand how they work. So I’m going to start explaining it.

Computers aren’t magic. They don’t hate you and they don’t cheat at video games. In fact, there’s not all that much going on in that box. All computers really do is store and manipulate numbers. In fact, they just store and manipulate two numbers: 1′s and 0′s. They just do it really fast and with a lot of them.

Binary Numbers
So let’s talk a little about those ones and zeros. As you know, we humans are used to working with numbers in groups of ten — probably because we have ten fingers and ten toes. It’s a natural number to us.

Two is a natural number to computers because computer are made of transistors. You’ve probably heard of a transistor. You probably know that it’s an electronic component and you probably know that transistors are the basic building blocks of computers. But what does a transistor do? Well, a transistor is just a microscopic switch. Switches, as you know, can either be on or off. If the switch is on, the computer interprets it as a one. If it’s off, it is a zero. When we work with numbers, we build them out of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. A computer only has two digits to work with: zero and one — off and on.

Making Numbers Out Of One’s And Zeros

Understanding binary numbers takes a little getting used to. I mean, we are really used to working with numbers in groups of ten. It’s not vital that you understand how binary numbers work, but it is pretty cool, so let’s spend some time with them.

When you count with your fingers, it’s easy to count to ten, but what do you do when you get past ten? You probably make a mental note that you’ve gotten to ten and start over again with one finger. Say every time you get to ten you make a tick mark on a piece of paper. That mark represents “one ten.” Then you can use your fingers to count to ten again, at which point you make another mark. Now you have “two tens.” When we write out numbers we call these collections of marks “digits.”

When you get to ten fingers (or “ten ones”) we simplify that and call it “one ten.” When you get to ten “tens” we can simplify that and call it one “hundred.” Ten hundreds are called one “thousand” and so forth. It’s all based on grouping things in tens. In fact, our system of counting is called “base-10″ or, to get all Latin-y: decimal.

So when we have a decimal number like 3,852, that can be described as:

2 “ones”
5 “tens”
8 “hundreds”
3 “thousands”

Since computers count based on the number 2, their system is called “base-2″ or “binary.” Counting binary is the same, but instead of grouping numbers by ones, tens, hundreds, thousands, etc, they are grouped into ones, twos, fours, eights, etc. Two “ones” is simplified as one “two.” Two “twos” are one “four.” Two “fours” is one eight… and so forth. Here’s an example of counting to 5 in binary:

eights  fours  twos  ones
0       0      0     0       = 0
0       0      0     1       = 1
0       0      1     0       = 2
0       0      1     1       = 3
0       1      0     0       = 4
0       1      0     1       = 5

A binary digit is known as a “bit.” (Binary digit. B-it. Get it?) With one decimal digit, you can count to 9, since 9 is the highest value one decimal digit can have. With two decimal digits, you can count to 99. With three, you can count to 999, and so forth.

With one bit, you can count to 1 since 1 is the highest value one binary bit can have. With two you can count to 3 because the binary number “11″ is 1 “one” and 1 “two.” With three digits (111) you have 1 “one”, 1 “two” and 1 “four” so you can count to seven (1+2+4).

You should now be able to comfortably laugh at this joke: “There are 10 types of people in the world: those who understand binary and those who don’t.” Har. Hee. Hoo.

Modern computers allow 64 bit numbers. That is, they use 64 transistors to store each numeric value. The highest number you can count to with 64 bits is 18,446,744,073,709,551,615. So… big.

Like I said, it takes a little while to get your head around binary numbers. Here’s what you need to take away from this: Computers are made of billions of transistors which can each store a 1 or a 0. Using ones and zeros, computers can count very high.

Hmmm. I feel like I only scratched the surface here. Next time I’ll explain how computers use bits to make things besides numbers like illegally downloaded mp3s and cat montage videos.

More Resources on Binary Numbers

Next Lesson: Everything is Numbers


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