Digital Systems: Principles and Design

BASIC CONCEPTS

2.1 DECIMAL NUMBER

A decimal number is a number based upon ten values: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Suppose

there are twelve apples. How can we represent twelve? One is that take one for each apple

and write 111111111111. Easier way is write 2 at the right most position and 1 at the left of

2 and assume that weight (w) of the left side digit is always ten times (w

d

= 10) compared to

the neighboring one on the right side. Now, the number 12 is twelve represented by only two

digits, 12 one digit is at right position (p = 0) and other is at the left position (p = 1). We get

a formula as under.

Value, 12 = 1 ´ w

d

1

+

2 ´ w

d

0

...(2.1)

Here ...