Definition

A binary number is a number expressed in the binary numeral system (i.e., base-2 numeral system). The binary numeral system only uses two symbols, usually 0 and 1.

Introduction

Computers use the binary number system. Each binary number is a bit. Groups of 8 bits are called a byte.

Convert binary numbers to decimal numbers

Binary numbers can be converted into decimal numbers by multiplying the binary value in each column (0 or 1) by the corresponding decimal value for the column.

Binary number colum	Decimal value
Right-most column	1
Second column from the right	2
Third column from the right	4
Forth column from the right	8
Fifth column from the right	16
Sixth column from the right	32
Seventh column from the right	64

For example, the binary number = 1011 1001 can be represented by the decimal number 185.

Binary value	1	0	1	1	1	0	0	1
Decimal value	128	64	32	16	8	4	2	1

(1 x 128) + (0 x 64) + (1 x 32) + (1 x 16) + (1 x 8) + (0 x 4) + (0 x 2) + (1 x 1) = 185

Another way to convert a binary number into a decimal number is to add together all the decimal numbers that are represented by a 1.

Identify decimal number value for each 1 in the binary number
Add decimal number values together from left to right

(128)+(32)+(16)+(8)+(1) = 185

Related terms

Bit

Byte

Decimal number

Hexadecimal number

Glossary

Binary number

Definition

Introduction

Related terms

Further reading