NUMBER BASES

NUMBER BASES
I will make the explanation to this topic very brief. A explanation that you find
difficult and challenging to understand please indicate by commenting please inthe
comment box below. It is going to be based on jamb syallabus and if you want me to
cover some aspects of other examination syallabus such as NECO,WAEC,SAT etc. It
wont be a problem to me if you indicate.

Based on JAMB syallabus you are expected to know the following on Number Bases
in Number and Numeration.
NUMBER BASES IN NUMBER
NUMERATION
OBJECTIVES
Operations in different number bases from 2
to 10
Candidates should be able to:
Conversion from one base to another
including fractional parts
1. Perform four basic operations(+,−,×,÷ )
2 .convert one base to another
Binary numbers are counting of a base to place value numbers i.e 0 and 1 e.g 01101two or 01101 base 2 .
Note that the one written in word is mostly preferred to the one written in figure to avoid
confusion of numbers.
To Convert Base Two Number System To Base Ten
e.g 110101two
Start by counting the numbers from the right hand side towards the left hand side
like this:
5 4 3 2 1 0
1 1 0 1 0 12 = 1    × 2^0 + 0 ×  2^1 + 1 × 2^2 + 0 × 2^3 + 1 × 2^4 + 1 × 2^5
= 1 + 0 + 4 + 0 + 16 + 32
= 53
Solve these:
1. 1256seven
2. 564eight
ANSWERS
1. 482
2. 372
BICIMALS
Base two fractions or bicimals are based on negative powers of ten.
e.g 1.101
Beginning from the number at the left hand side we have:
1×10^0+1×10^-1+ 0×10^-2+1×10^-3
EXAMPLES
Convert the following below from bicimals to decimals
1. 1.101
2. 110.11
SOLUTION
1) 1.101= 1×10^0+1×10^-1+ 0×10^-2+1×10^-3
= 1 + 0.5 + 0 + 0.125
    = 1.625
2) I will leave the second example as a practice question for you all,
though the answer is 6.75. Cheers in advance to those of you that
got the drill.
Quiz Question
Let me see the maths whiz in you:
Convert the answers we got above from decimals to bicimals (show
your workings)
In the next post which is the end to Number bases I will show you
how to treat the topic better, as I will put a finishing touch to
Number Bases. You are on your way to becoming an high flying
student in any examination, Just stay updated.