# Number System

**Binary-Decimal Conversion**

Example

Find the decimal equivalent of binary number 11111.

Solution

The equivalent decimal number is,

= 1 Ã— 2

= 16 + 8 + 4 + 2 + 1 = ( 31 )

= 1 Ã— 2

^{4}+ 1 Ã— 2^{3}+ 1 Ã— 2^{2}+ 1 Ã— 2^{1}+ 1 Ã— 2^{0}= 16 + 8 + 4 + 2 + 1 = ( 31 )

_{10}

**Decimal-to Binary Conversion**

Example

Express the 25.5 decimal number in the binary form.

Solution

Integer Part:

Thus, (25)

Read down to up

Fraction part

Therefore 25.5

Thus, (25)

_{10}= (11001)_{2}Read down to up

Fraction part

*i.e.,*0.5_{10}= 0.1_{2}Therefore 25.5

_{10}= 11001.1_{2}

**Decimal-Octal Conversion**

This can be achieved by dividing the given decimal number repeatedly by 8, until a quotient of 0 is obtained.

Example

Convert conversion (444.499)

_{10}.Solution

On reading the remainders from bottom to top, the decimal (444)

_{10}(674)

_{8}. Now, fractional conversion

**Multiplication Generated Integer**

The process gets terminated when significant digits are acquired. Thus, octal equivalent is (444.499)

_{10 }= (674.3773)

_{8}

**Octal-Binary Conversion**

It can be explained through the following example: To convert (377)_{8} into binary, replace each significant digit by its 3-bit binary equivalent.

Binary-Hexadecimal Conversion

e.g., (10100110111110)_{2} = (0010 1001 1011 1110)_{2} = (2 9 B E)_{16} Ã— 1

Hexadecimal-Binary Conversion

It can be explained through an example. To convert (1D5)_{16} into binary, replace each significant digit by its 4-bit binary equivalent.