# 10th Class Computers Classification of Computer and Number System Binary Number System

## Binary Number System

Category : 10th Class

### Binary Number System

A number system with a base-2 is known as binary number system. The whole binary number system depends on two digits these are 0 and 1, respectively. By using these two digits the numbers in binary number system are written. Thus the place value of a digit in a number increases in the power of 2 from right to left. The following example shows how to convert binary number 1010101 to decimal number:

 Power of             2              6              5              4              3              2              1              0 Binary number                  1              0              1              0              1              0              1

The place value of 1 is: $1*{{2}^{0}}=1$

The place value of 0 is: $0*{{2}^{1}}=0$

The place value of 1 is: $1*{{2}^{2}}=4$

The place value of 0 is: $0*{{2}^{3}}=0$

The place value of 1 is: $1*{{2}^{4}}=16$

The place value of 0 is: $0*{{2}^{5}}=0$

The place value of 1 is: $1*{{2}^{6}}=64$

The decimal number = 1 + 4 + 16 + 64 = 85

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