Change of binary number to decimal number and decimal number to binary number

Binary Number System

Digital computer represents all kinds of data and information in the binary system. Binary Number System consists of two digits 0 and 1. Its base is 2. Each digit or bit in binary number system can be 0 or 1. A combination of binary numbers may be used to represent different quantities like 1001. The positional value of each digit in binary number is twice the place value or face value of the digit of its right side. The weight of each position is a power of 2.

The place value of the digits according to position and weight is as follows:

Position |
3 |
2 |
1 |
0 |

Weights |
23 |
22 |
21 |
20 |

Example: Convert 101112 decimal number

Position |
2 |
1 |
0 |
-1 |
-2 |

Weights |
102 |
101 |
100 |
10-1 |
10-2 |

Face Value |
1 |
3 |
9 |
7 |
8 |

101112 = 1 x 24 + 0 x 23 + 1 x 22 + 1 x 21 + 1 x 20

= 1 x 16 + 0 + 1 x 4 + 1 x 2 + 1 x 1

= 16 + 0 + 4 2 + 1

= 2310

Decimal number system

The Decimal Number System consists of ten digits from 0 to 9. These digits can be used to represent any numeric value. The base of decimal number system is 10. It is the most widely used number system. The value represented by individual digit depends on weight and position of the digit.

Each number in this system consists of digits which are located at different positions. The position of first digit towards left side of the decimal point is 0. The position of second digit towards left side of the decimal point is 1. Similarly, the position of first digit towards right side of decimal point is -1. The position of second digit towards right side of decimal point is -2 and so on.

The value of the number is determined by multiplying the digits with the weight of their position and adding the results. This method is known as expansion method. The rightmost digit of number has the lowest weight. This digit is called Least Significant Digit (LSD). The leftmost digit of a number has the highest weight. This digit is called Most Significant Digit (MSD). The digit 7 in the number 724 is most significant digit and 4 is the least significant digit.

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Decimal to binary conversion examples

(51)_{10} = (110011)_{2}

(217)_{10} = (11011001)_{2}

(8023)_{10} = (1111101010111)_{2}