**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,

Table of Contents

**Different number bases/system **

- Binary system
- Octal system
- Denary/decimal system
- Hexadecimal system

**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.

**Octal System**

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

**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

**Hexadecimal System**

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.

- Convert 17
_{ten }to base 2

2 17

2 8 r 1

2 4 r 0 17_{ten} = 10001_{2}

2 2 r 0

2 1 r 0

0 r 1

- Convert 58
_{ten}to base 2

2 58

2 29 r 0

2 14 r 1

2 7 r 0 58_{ten} = 111010_{2}

2 3 r 1

2 1 r 1

0 r 1

- Convert 248
_{ten}to octal

8 248

8 31 r 0

8 3 r 7 248_{ten} = 370_{eight}

0 r 3

- Convert 312
_{ten}to base 16

16 312

16 19 r 8

16 1 r 3 312_{ten} = 138_{16}

0 r 1

- Convert 935
_{ten}to hexadecimal

16 935

16 58 r 7

16 3 r A 935_{ten} = 3A7_{16}

0 r 3

**EVALUATION**

- Convert 25
_{ten}to binary - Convert 174
_{ten}to octal - Convert 381
_{ten}to hexadecimal - Convert 19
_{ten}to binary