• • The following examples illustrate how to convert hexadecimal number to a decimal numberExample

    Convert octal number 321₈ to its binary equivalent

    Solution

    Working from left to the right, each octal number is represented using three digits and then combined we get the final binary equivalent. Therefore:

    3=011₂

    2=010₂

    1=001₂

    Combining the three from left to right

    3	2	1
    011	010	001

    321₈ =011010001₂

    Converting binary numbers to hexadecimal numbers

    • To convert binary numbers to their binary equivalents, simply group the digits of the binary number into groups of four from right to left e.g. 11010001.The next step is to write the hexadecimal equivalent of each group e.g.

    1101- D

    0001- 1

    The equivalent of 11010001 is D1H or D1₁₆

    Converting hexadecimal numbers to decimal and binary numbers.

    Converting hexadecimal numbers to decimal number

    • To convert hexadecimal number to base 10 equivalent we proceed as follows:
    1. First, write the place values starting from the right hand side.
    2. If a digit is a letter such as ‘A’ write its decimal equivalent
    • Multiply each hexadecimal digit with its corresponding place value and then add the products

  The binary equivalent of the fractional part is extracted from the products by reading the respective integral digits from the top downwards as shown by the arrow next pag

• Combine the two parts together to set the binary equivalent.

Convert 0.375₁₀ into binary form

Read this digits

0.375×2=0.750

0.750×2=1.500

0.500×2=1.000 (fraction becomes zero)

Therefore 0.375₁₀=0.011₂

Converting octal numbers to decimal and binary numbers

Converting octal numbers to decimal numbers

• To convert a base 8 number to its decimal equivalent we use the same method as we did with binary numbers. However, it is important to note that the maximum absolute value of a octal digit is 7.For example 982 Is not a valid octal number because digit 9 is not an octal digit, but 736₈ is valid because all the digits are in the range 0-7.Example shows how to convert an octal number to a decimal number.

Example 1.13

Convert 512₈ to its base 10 equivalent

Solution

Place value	82	81	80
	64	8	1
Octal digit	5	1	2

Write each number under its place value as shown below

Multiply each number by its place value.

N10=(5 x 82)+(1 x 81 )+(2 x 80 ) =(5 x 64)+8+2 =320+8+2 N10=33010

64 x 5=320

8 x 1= 8

1 x 2=+ 2

330

Therefore512₈ =330₁₀

Converting octal numbers to binary numbers

• To convert an octal number to binary, each digit is represented by three binary digits because the maximum octal digit i.e. 7 can be represented with a maximum of seven digits. See table:

Octal digit	Binary equivalents
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111