Conversions

 

Binary to decimal numbers

To convert a binary number to a decimal number, add up the place values that have 1.

Example

        Convert 10011011 to decimal

Copyright © 2015 - NCS Pearson

 

Decimal to binary numbers

To convert a binary number to a decimal number, the place values in the binary system are used to create a sum of numbers that equal the value of the decimal number being converted.

Example

Copyright © 2015 - Prentice-Hall, Inc.

 

Octal to decimal numbers

To convert any octal number into decimal number, multiply the digits of the number from right hand side with increasing powers of 8 starting from 0 and finally sum up all the products.

Example

        Convert 123₈ to decimal

                   123₈ = 1x8² + 2x8¹ + 3x8⁰

                        =   64   +   16  +   3

  =   73

        The decimal equivalent of 123₈ = 73₁₀

 

Decimal to octal numbers

To convert any decimal number into an octal number, divide it by 8. The remainder is again divided by the largest possible power of 8. Continue the process until the power of 8 is 1 and the remainder is less than 8. Finally arrange the obtained quotient.

Example

        Convert 796₁₀ to octal

796/8 = 99 (remainder 4)

99.5/8 = 12 (remainder 3)

 12/8 = 1 (remainder 4)

   1/8 = 0 (remainder 1)

        The octal equivalent of 796₁₀ = 1434₈

 

Octal to binary numbers

To convert an octal number to binary number, look up each digit to obtain the equivalent group of three binary digits.

Example

        Convert 345₈ to binary

3      4      5

011   100   101

        The binary equivalent of 345₈ = 011100101₂

 

Decimal to hexadecimal numbers

To convert a decimal number to hexadecimal number, divide the number by 16 writing the remainders as hex characters and read that column from the bottom.

Example

        Convert 921₁₀ to hexadecimal

921/16 = 57 (remainder 9)

57/16 = 3 (remainder 9)

  3/16 = 0 (remainder 3)

        The hexadecimal equivalent of 921₁₀ = 399₁₆

 

Hexadecimal to binary numbers

To convert any hexadecimal number to binary number, convert each hex digit to 4 binary digits according to the standard table.

Example

        Convert 4E₁₆ to binary

4              E

0100         1110

        The binary equivalent of 4E₁₆ = 01001110₂

 

BCD to decimal numbers

To convert any BCD number into decimal number, simply split the number into groups of four and convert according to the standard table.

Example

        Convert 10000011 to decimal

1000         0011

8              3

        The decimal equivalent of 10000011 = 83₁₀

 

Note: The required standard conversion tables can be found in the related sub-topics in ‘Numbering Systems’ section.