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