Page 11 - DCAP104_EXPOSURE_TO_COMPUTER_DISCPLINES
P. 11
Exposure to Computer Disciplines
Notes 1.2 Data Representation in Computer
Introduction data representation considers how a computer uses numbers to represent data inside
the computer. Three types of data are considered at this stage: 1. Numbers including positive,
negative and fractions. 2. Text. 3. Graphics.
1.2.1 Decimal Representation in Computers
The binary number system is most natural for computer because of the two stable states of
its components. But, unfortunately, this is not a very natural system for us as we work with
decimal number system. Then how does the computer do the arithmetic? One of the solutions,
which are followed in most of the computers, is to convert all input values to binary. Then the
computer performs arithmetic operations and finally converts the results back to the decimal
number so that we can interpret it easily. Is there any alternative to this scheme? Yes, there
exist an alternative way of performing computation in decimal form but it requires that the
decimal numbers should be coded suitably before performing these computations. Normally,
the decimal digits are coded in 6-8 bits as alphanumeric characters but for the purpose of
arithmetic calculations the decimal digits are treated as four bit binary code. As we know 2
binary bits can represent 2’ = 4 different combination, 3 bits can represent 23 = 8 combination
and 4 bits can represent 24 = 16 combination. To represent decimal digits into binary form
we require 10 combinations only, but we need to have a 4-digit code. One of the common
representations is to use first ten binary combinations to represent the ten decimal digits.
These are popularly known as Binary Coded Decimals (BCD). The following representation
shows the binary coded decimal numbers. Let us represent 43.125 in BCD. It is 0 100 00 1
1.000 1 .00 10 01 0 1
Decimal Binary Coded Decimal
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
10 0001 0000
11 0001 0001
12 0001 0010
13 0001 0011
.. ........
20 0010 0000
.. ........
30 0011 0000
4 LOVELY PROFESSIONAL UNIVERSITY
