Binary describes a numbering scheme in which there are
only two possible values for each digit: 0 and 1. The term also refers to any digital encoding/decoding system in which there
are exactly two possible states.In digital data memory,
storage, processing, and communications, the 0 and 1 values are sometimes called
“low” and “high,” respectively.
Binary numbers look strange when they are written out directly.This is because
the digits’ weight increases by powers of 2, rather than by powers of 10.In a
digital numeral, the digit furthest to the right is the “ones” digit; the next
digit to the left is the “twos” digit; next comes the “fours” digit,
then the “eights” digit, then the “16s” digit, then the
“32s” digit, and so on.The decimal equivalent of a binary number can be
found by summing all the digits.For example, the binary 10101 is equivalent to the
decimal 1 + 4 + 16 = 21:
| DECIMAL = 21 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| BINARY = 10101 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
The numbers from decimal 0 through 15 in decimal, binary, octal, and hexadecimal
form are listed below.
| DECIMAL | BINARY | OCTAL | HEXA-
DECIMAL |
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 6 | 110 | 6 | 6 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
