Form 1 · Chapter 2

The Binary Number System

Computers store everything using only 0 and 1. Learn how binary works and how to convert between binary and decimal.

Two digits are enough

People count using the decimal system with ten digits, 0 to 9. A computer is made of tiny switches that are either off or on. Because there are only two states, the computer uses the binary number system, which has just two digits: 0 and 1. Each 0 or 1 is called a bit (binary digit). Everything you see on a screen — numbers, letters, pictures and sound — is stored as a pattern of bits.

Place values

In decimal, each column is worth ten times the one on its right. In binary, each column is worth two times the one on its right: 1, 2, 4, 8, 16, and so on. To read a binary number, add up the place values where a 1 appears.

Key idea

Binary place values from the right are 1, 2, 4, 8. So 1010 = 8 + 0 + 2 + 0 = 10 in decimal.

Converting numbers

To change binary to decimal, write the place values above each bit and add the ones with a 1. To change decimal to binary, ask how many 8s, 4s, 2s and 1s fit. For example, decimal 5 needs one 4 and one 1, so it is 0101. With 4 bits you can make any value from 0 (0000) up to 15 (1111).

Example

Binary 1100 = 8 + 4 + 0 + 0 = 12. Binary 0011 = 0 + 0 + 2 + 1 = 3. Decimal 6 = one 4 + one 2 = 0110.

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