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 301_four to a base six number.

Solution

First 301_four will be converted to a base ten number

301_four = 3 × 4² + 0 × 4¹ + 1 × 4⁰

= 48 + 0 + 1

= 49_ten

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

301_four = 121_six

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 2210_three to a base five number
2. Convert 5201_seven 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.