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# NUMBER BASE SYSTEM

CONTENT

1. Conversion of numbers from one base to another
2. Addition, subtraction, division and multiplication of number bases
3. Application to computer programming

## CONVERSION OF NUMBERS FROM ONE BASE TO ANOTHER BASE

To convert from a base to another you may have to pass through base ten.

Example 1: Convert 301four to a base six number.

Solution

First 301four will be converted to a base ten number

301four = 3 × 42 + 0 × 41 + 1 × 40

= 48 + 0 + 1

= 49ten

49ten will now be converted to a base six number by repeated division

301four = 121six

Example 2: convert 1101112 to base 5.

Solution

1101112 = 1 × 25+ 1 × 24 +0 × 23 + 1 × 22 + 1 × 21 + 1 × 20

= 1 × 32 + 1 × 16 + 0 × 8 + 1 × 4 + 1 × 2 + 1 × 1

= 32 + 16 + 0 + 4 +2 +1

= 5510

Then we convert 5510 to a number in base 5

Hence, 5510 = 2105

CLASS ACTIVITY

1. Convert 2210three to a base five number
2. Convert 5201seven to a binary (base two) number

## ADDITION, SUBTRACTION AND MULTIPLICATION OF NUMBER BASES

Operation in other bases other than base ten are carried out in a manner similar to what is obtained in base ten.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS1 General Mathematics, SS1 General Mathematics Evaluation Questions, SS1 General Mathematics Evaluation Questions First Term, SS1 General Mathematics First Term, SS1 General Mathematics Objective Questions, SS1 General Mathematics Objective Questions First Term
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