C Primer Plus®, Third Edition

Binary Numbers, Bits, and Bytes

The usual way to write numbers is based on the number 10. For instance, 2,157 has a 2 in the thousands place, a 1 in the hundreds place, a 5 in the tens place, and a 7 in the ones place. This means you can think of 2,157 as being the following:

2 x 1000 + 1 x 100 + 5 x 10 + 7 x 1

However, 1,000 is 10 cubed, 100 is 10 squared, 10 is 10 to the first power, and, by convention, 1 is 10 (or any positive number) to the zero power. Therefore, you can also write 2,157 as this:

2 x 103 + 1 x 102 + 5 x 101 + 7 x 100
				

Because our system of writing numbers is based on powers of ten, we say that 2,157 is written in base 10.

Presumably, the decimal system evolved because we have ten fingers. A computer bit, in a sense, has ...