Binary number
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
Decimal number
Hexadecimal number
Further reading
Carrier, Brian. Computer foundations (chapter 2). In File system forensic analysis. Boston: Pearson Education (2005): 17-45.