Our familiar decimal number system is based on powers of 10. The number 123 is actually 100 + 20 + 3 or 1 × 102 + 2 × 101 + 3 × 100.
The binary number system is based on powers of 2. The number 1001012 (that is, ``100101 base two'') is 1 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 1 × 20 or 32 + 4 + 1 or 37.
We usually speak of the individual numerals in a decimal number as digits, while the ``digits'' of a binary number are usually called ``bits.''
Besides decimal and binary, we also occasionally speak of octal (base 8) and hexadecimal (base 16) numbers. These work similarly: The number 458 is 4 × 81 + 5 × 80 or 32 + 5 or 37. The number 2516 is 2 × 161 + 5 × 160 or 32 + 5 or 37. (So 3710, 1001012, 458, and 2516 are all the same number.)
Read sequentially: prev next up top
This page by Steve Summit // Copyright 1995, 1996 // mail feedback