Page 31 - DCAP101_BASIC_COMPUTER_SKILLS

Basic Computer Skills

Notes 2.2 Converting from One Number System to Another

Numbers expressed in decimal number system are much more meaningful to us, than are
numbers expressed in any other number system. This is because we have been using decimal
numbers in our day-to-day life, right from childhood; however, we can represent any
number in one number system in any other number system. Because the input and final
output values are to be in decimal, computer professionals are often required to convert
number in other systems to decimal and vice-versa. Many methods can be used to convert
numbers from one base to another. A method of converting from another base to decimal,
and a method of converting from decimal to another base are described below.

2.2.1 Converting from Another Base to Decimal
The following steps are used to convert a number in any other base to a base 10 (decimal)
number:
Step 1: Determine the column (positional) value of each digit (this depends on the
position of the digit and the base of the number system).
Step 2: Multiply the obtained column values (in Step 1) by the digits in the corresponding
columns.
Step 3: Sum up the products calculated in Step 2. The total is the equivalent value in
decimal.

1: 11001 = ?
2 10
Step 1: Determine column Values
Column Number Column
0
(From Right) 2 = 1
1
1 2 = 2
2
2 2 = 4
3
3 2 = 8
4
4 2 = 16
Step 2: Multiply the column values by the corresponding column digits.
16 8 4 2 1
x1 x1 x0 x0 x1
16 8 0 0 1
Step 3: Sum up the products
16 + 8 + 0 + 0 + 1 = 25
Hence, 11001 =25
2 10
2: 4706 = ?
8 10
Step 1: Determine column values
Column Number Column
(From Right)
0
1 8 = 1
1
2 8 = 8
2
3 8 = 64
3
4 8 = 512

24 LOVELY PROFESSIONAL UNIVERSITY