NUMBER CONVERSION

NUMBER CONVERSION

Decimal to Binary: At first we need to divide the given decimal number by two and remind the retain. The step as below.

Ex: if the given number is (146)₁₀, then

156/2 = 78 and retain = 0

78/2   = 39 and retain = 0

39/2   = 18 and retain = 1

19/2   = 9   and retain = 1

9/2     = 4 and retain   = 1

4/2     = 2 and retain   = 0

2/2     = 1 and retain   = 0

So, the Binary Number is (10011100)₂

Octal to Binary:

Octal to Binary

• At first separate the octal number if it is more than one digit.

              Ex:     7    6     3    1

• Find the binary number for each digit of octal number. Add “0” to the left if binary number is shorter than 3 bits.

              Ex:      7              6           3         1

                        111       110      011      001

• Writ the all groups binary number together, maintaining the same group order provides the binary for given octal number.

Ex: 111110011001

Result: (7631)₈ = (111110011001)₂

Hexadecimal to Binary: If the given number is more than one digit, then

          Ex: (3AB2)₁₆

• Separate the Hexadecimal number individual

          Ex:     3         A           B           2

• Write Binary number for each digit of hexadecimal number.

Ex:

Hexadecimal to Binary

• So the result is (3AB2)₁₆ = (11101010110010)₂

Binary to Decimal:

If the given number is (101011)_2, then

=1 x 2⁵ + 0 x 2⁴ + 1 x 2³ + 0 x 2² + 1 x 2¹ + 1 x 2⁰

= 32 + 0 + 8 + 0 + 2 + 1

=42

So the result is (42)₁₀

Octal to Decimal:

If the given number is (5011)_8, then

=5 x 8³ + 0 x 8² + 1 x 1¹ + 1 x 2⁰

= 2560 + 0 + 1 + 1

= 2562

So the result is (2562)₁₀

Hexadecimal to Decimal:

If the given number is (1E1C12)_2, then

=1 x 16⁵ + E x 16⁴ + 1 x 16³ + C x 16² + 1 x 16¹ + 2 x 16⁰

= 1048576 + 15 x 65536 + 4096 + 12 x 256 + 16 + 32

= 2038832

So the result is (2038832)₁₀