ECSE-2610
Computer Components & Operations
(CoCO)
Fall 2006
Part 2:
Number Systems

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Decimal Representation:
10 digits = {0,1,2,...,9}
Positional Number Notation:
Positional Number Notation:
Weight of each digit determined by its position.
Example:
246 = 200
+ 40
+ 6
= 2 x 10
2
+ 4 x 10
1
+ 6 x 10
0
In general, for the Base 10 representation:
N
=
Σ
N
i
x 10
i
where each
N
i
∈
{0, 1, 2, . . . , 9} is the weight on the
base raised to the exponent
i
.
Note:
Decimal fractions occur when
i
is negative:
0.35 = 3 x 10
-1
+ 5 x 10
-2