Example

Convert the hexadecimal number 111₁₆ to its binary equivalent.

Solution

Place each number under its place value.

162	161	160
1	1	1

256 x1= 256

16 x 1 = 16

1 x 1= + 1

273

Therefore 111₁₆ =273₁₀

Example

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:

First, write the place values starting from the right hand side.

1. 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 following examples illustrate how to convert hexadecimal number to a decimal number

Example

Convert the hexadecimal number 111₁₆ to its binary equivalent

Solution

Place each number under its place value.

162	161	160
1	1	1

256 x1= 256

16 x 1 = 16

1 x 1= + 1

273

Therefore 111₁₆ =273₁₀