Embedded Files
NUMBER BASES
Introduction:
A number base is the number of digits or combination of digits that a system of counting uses to represent numbers. A base can be any whole number greater than 0. The most commonly used number system is the decimal system, commonly known as base 10. In everyday life, we count or estimate quantities using groups of ten items or units. This may be so because, naturally, we have ten ngers. For example, when we count ten, i.e. we write 10 meaning one group of 10 and no units. A quantity like twenty five, written as 25 means 2 groups of 10 and 5 units.
Suppose instead we had say 6 fingers.
How, in your opinion would we do our counting?
If we had eight fingers, how would we count?
This is now what we are to cover under this topic.
NOTE:
The digits of a number in any base are less than the base itself.
The digits 10 and 11 are represented by t and e respectively in number bases.
For digits above 11 are represented by alphabetic letters of your choice
The names of some number systems is as given below.
1.1 Identifying numbers of different bases on an abacus.
In your primary education, you studied number bases such as bases five, two and ten (decimal base). Remember the numerals for all the various number bases you studied by doing the following activity:
Activity 1. 1: Getting familiar with number bases
In your groups, identify situations in which you have ever used number bases in your life.
1.2 Place Values Using the Abacus
The representation of numbers on an abacus helps in identifying the place value of digits in any base
1.3 Converting Numbers
Numbers can be converted from one base to another, and when you do this, you get the same numbers written in different bases.
1.3.1 Converting from any base to base ten
EXAMPLES
Convert the following to base ten:
Exercise.
1.3.2 Converting from base ten to other bases
We use BNR
Divide the number repeatedly by the required bases
The remainder in reverse order gives the required number
Exercise Set
1.4: Operation on Numbers in Various Bases
1.4.1 Addition of bases.
EXAMPLE
1.4.2 Subtraction of bases
EXAMPLE
1.4.3 Multiplication of bases
EXAMPLE:
1.4.4 Division of bases
Convert each number base to base ten
Divide the two numbers in base ten
Convert the result back to the required base
Exercise.
Situation of Integration
A community is hit by famine and the government decides to give each member in the household a potato to solve their problem of hunger.
Support: Each package contains an equal number of potatoes of five.
There are 10 households in the community with 3, 5, 7, 4, 6, 5,8,12, 13 members respectively.
Resources: Knowledge of Bases, knowledge of mathematical operations
Task: Determine the number of packages of potatoes the government will take to that community. In case there are remaining potatoes, discuss what the government should do with them.
Page updated
Report abuse