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
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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.
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Octal System
This is counting in eight i.e. base 8. It has 0,1,2,3,,4,5,6,7 digits.
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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
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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 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
- 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
- Convert 248ten to octal
8 248
8 31 r 0
8 3 r 7 248ten = 370eight
0 r 3
- Convert 312ten to base 16
16 312
16 19 r 8
16 1 r 3 312ten = 13816
0 r 1
- Convert 935ten to hexadecimal
16 935
16 58 r 7
16 3 r A 935ten = 3A716
0 r 3
EVALUATION
- Convert 25ten to binary
- Convert 174ten to octal
- Convert 381ten to hexadecimal
- Convert 19ten to binary