**NUMBER BASE SYSTEM**

CONTENT

- Conversion of numbers from one base to another
- Addition, subtraction, division and multiplication of number bases
- Application to computer programming

**CONVERSION OF NUMBER****S**** 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 × 4^{2} + 0 × 4^{1} + 1 × 4^{0}

= 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 110111_{2 }to base 5.

**Solution**

110111_{2 }= 1 × 2^{5}+ 1 × 2^{4} +0 × 2^{3} + 1 × 2^{2} + 1 × 2^{1 }+ 1 × 2^{0}

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

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

= 55_{10}

Then we convert 55_{10} to a number in base 5

Hence, 55_{10} = 210_{5}

**CLASS ACTIVITY**

- Convert 2210
_{three }to a base five number - 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.

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