Binary and decimal
The decimal system is base 10 and uses ten digits (0 to 9). The binary system is base 2 and uses only two digits, 0 and 1. Computers store data in binary because a circuit is easily set to "off" (0) or "on" (1).
In binary, each position has a place value that doubles from right to left: 1, 2, 4, 8, 16, and so on. To find the decimal value, add the place values wherever there is a 1. Being confident with both systems helps you understand how the numbers you type are actually stored inside a computer.
Example
Convert 10112 to decimal:
(1×8) + (0×4) + (1×2) + (1×1) = 8 + 0 + 2 + 1 = 11.
Decimal to binary
To change a decimal number to binary, repeatedly divide by 2 and write the remainders from bottom to top. You can also subtract the largest place values that fit.
Example
Convert 13 to binary using place values 8, 4, 2, 1:
13 = 8 + 4 + 1, so the bits are 1101.
Answer: 13 = 11012.
Handy data units
A single binary digit is a bit. Four bits make a nibble, and eight bits make one byte. A 4-bit number can store values from 00002 (0) up to 11112 (15).
Remember
- Binary is base 2; the digits are only 0 and 1.
- Place values double: 1, 2, 4, 8, 16 …
- 10112 = 11 and 13 = 11012.