# NUMBER BASES

## NUMBER BASES

Number bases refer to ways of counting numbers. Counting started way back in the ancient times when began counting first, with his fingers. He counts in tens maybe because he has ten fingers and this is called decimal system of counting. There are different bases of counting,

## Different number bases/system

1. Binary system
2. Octal system
3. Denary/decimal system

1. ## Binary System

The word BI means two, so binary combination means numbers made up of a combination of only two numbers. It is also refers to numbers in base 2.  The available digits in binary system where 0 means off and 1 means ON.

1. ## Octal System

This is counting in eight i.e. base 8. It has 0,1,2,3,,4,5,6,7 digits.

1. ## Denary/Decimal

This is counting in tens. They are also called decimal system. The decimal system has the following digits 0,1,2,3,4,5,6,7,8,9

This system deals with numbers in base 16. It has the following digits 0,1,2,3,4,5,6,7,8,9,A,B,C,D.E,F (A=10, B=11, C=12, D=13, E=14 and F=15).

## CONVERSION FROM BASE TEN TO OTHER BASES

To convert a number in decimal system to other bases, the method of continuous division of the number by the new base number is used.

1. Convert 17ten to base 2

2         17

2          8  r  1

2          4  r  0                             17ten = 100012

2          2  r  0

2          1  r  0

0  r  1

1. Convert 58ten to base 2

2          58

2          29  r  0

2          14  r  1

2          7  r  0                          58ten = 1110102

2          3  r  1

2          1  r  1

0  r  1

1. Convert 248ten to octal

8          248

8          31   r  0

8          3    r   7              248ten = 370eight

0    r  3

1. Convert 312ten to base 16

16       312

16       19   r  8

16       1     r  3                   312ten = 13816

0    r  1

16       935

16       58    r 7

16       3      r A                    935ten = 3A716

0      r 3

## EVALUATION

1. Convert 25ten to binary
2. Convert 174ten to octal