The Base-2 System and the 8-bit Byte

The reason computers use the base-2 system is because it makes it a lot easier to implement them with current electronic technology. You could wire up and build computers that operate in base-10, but they would be fiendishly expensive right now. On the other hand, base-2 computers are relatively cheap.

So computers use binary numbers, and therefore use binary digits in place of decimal digits. The word bit is a shortening of the words "Binary digIT." Whereas decimal digits have 10 possible values ranging from 0 to 9, bits have only two possible values: 0 and 1. Therefore, a binary number is composed of only 0s and 1s, like this: 1011. How do you figure out what the value of the binary number 1011 is? You do it in the same way we did it above for 6357, but you use a base of 2 instead of a base of 10. So:

(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11

You can see that in binary numbers, each bit holds the value of increasing powers of 2. That makes counting in binary pretty easy. Starting at zero and going through 20, counting in decimal and binary looks like this:

 0 =     0
 1 =     1
 2 =    10
 3 =    11
 4 =   100
 5 =   101
 6 =   110
 7 =   111
 8 =  1000
 9 =  1001
10 =  1010
11 =  1011
12 =  1100
13 =  1101
14 =  1110
15 =  1111
16 = 10000
17 = 10001
18 = 10010
19 = 10011
20 = 10100

When you look at this sequence, 0 and 1 are the same for decimal and binary number systems. At the number 2, you see carrying first take place in the binary system. If a bit is 1, and you add 1 to it, the bit becomes 0 and the next bit becomes 1. In the transition from 15 to 16 this effect rolls over through 4 bits, turning 1111 into 10000.

Bits are rarely seen alone in computers. They are almost always bundled together into 8-bit collections, and these collections are called bytes. Why are there 8 bits in a byte? A similar question is, "Why are there 12 eggs in a dozen?" The 8-bit byte is something that people settled on through trial and error over the past 50 years.

With 8 bits in a byte, you can represent 256 values ranging from 0 to 255, as shown here:

  0 = 00000000
  1 = 00000001
  2 = 00000010
   ...
254 = 11111110
255 = 11111111

In the article How CDs Work, you learn that a CD uses 2 bytes, or 16 bits, per sample. That gives each sample a range from 0 to 65,535, like this:

    0 = 0000000000000000
    1 = 0000000000000001
    2 = 0000000000000010
     ...
65534 = 1111111111111110
65535 = 1111111111111111

Next, we'll look at one way that bytes are used.