Counting in Different Number Bases

A number base is a system of counting in which certain units make up a “bundle”. The "bundle" will form the next place value and the placing of the digits shows the value.

In number bases, counting is done in base ten. Base ten is sometimes called DECIMAL or DENARY.

Also it should be noted that base two is otherwise called BINARY.

Students should also note that when solving problems under number bases, the base in use should always be written in words and not figures.

For example; 233_eight, 87_six, ….

The placing of the digits shows the place value. For example; 6578_ten stands for 6 thousands, 5 hundreds, 7 tens, 8 units.

= 6 x 1000 + 5 x 100 + 7 x 10 + 8 x 1

= 6 x 10³ + 5 x 10² + 7 x 10¹ + 8 x 10⁰

Also 246_seven = 2 x forty nines, 4 sevens, 6 units.

= 2 x 49 + 4 x 7 + 6 x 1

= 2 x 7² + 4 x 7¹ + 6 x 7⁰

Please note that number base is calculated in its own power, e.g. base ten in powers of ten, base three in powers of three and so on.

Examples;

1. 476_eight

= 4 sixty four 7 eights, 6 units

= 4 x 64 + 7 x 8 + 6 x 1 
= 4 x 8² + 7 x 8¹ + 6 x 8⁰

2. 24013_five 

= 2 six hundred and twenty five, 4 one hundred and twenty five, 0 twenty five, 1 fives, 3 units

= 2 x 5⁴ + 4 x 5³ + 0 x 5² + 1 x 5¹ + 3 x 5⁰