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