Computer Applications in Business - a fundamental course of computer science

1. M. Raihan
Email: rianku11@gmail.com

2. Data Representation
Part-3

3. Excess-3 Code
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It is a binary code in which each decimal number
is expressed in excess of three, i.e., 3
It is said to be self-complementing code (a code is
said to be self-complementing if the code word of
the 9’s complement of N, i.e., (9 – N) can be
obtained from the code word of N, interchanging all
the 1’s and 0’s).
The BCD code is not self-complementing.

4. Excess-3 Code
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Say, N = 7 = (1010)E3
Now 9 – N = 9 – 7 = 2
And 2 = (0101)E3
1’s complement of
(1010)E3 is (0101)E3 = 2
It is a non-weighted
code.
Decimal Digit Excess-3
0 0 0 1 1
1 0 1 0 0
2 0 1 0 1
3 0 1 1 0
4 0 1 1 1
5 1 0 0 0
6 1 0 0 1
7 1 0 1 0
8 1 0 1 1
9 1 1 0 0

5. Gray Code
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The Gray code is an un-weighted code not suited to
arithmetic operations.
It is useful for I/O devices, analog to digital
converters.
Each gray code differs from its neighbor by a single
bit.
Codes which have such a property is known as
cyclic code.

6. Binary to Gray Code
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The MSD of gray code is the same as the MSD of binary
code.
Add each pair of adjacent bits (starting from MSD) of the
binary code to get the next gray digit disregarding the
carries.

7. Gray Code to Binary
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MSD of the gray code is the MSD of binary.
Starting from MSD, produce bi+1=bi+gi+1 disregarding the
carries.

8. Error Detecting Code
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Computers are very reliable, but errors may be occurred
during data input, processing, output operation, or data
communication.
Errors may be caused by dust particles on storage media,
by improper humidity levels or by electrical disturbances
during data transmission between units.
Method for detecting errors by adding an extra bit to each
bit string of usually 7 bits.
This additional bit is called parity bit.

9. Error Detecting Code
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This checking feature is called a parity checking.
There are two types of parity checking codes: (i) Odd parity
code, and (ii) Even parity code.
In Odd parity method, the value of parity bit is chosen so that the
total number of 1’s in the code group (bit string plus parity bit) is
an odd number.
In Even parity method, the value of parity bit is chosen so that
the total number of 1’s in the code group (bit string plus parity
bit) is an even number.

10. Representation of Characters
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Coding of characters has been standardized to
facilitate exchange of recoded data between
computers.
Two popular standard codes:
EBCDIC (Extended Binary Coded Decimal
Interchange Code)
ASCII (American Standard Code for Information
Interchange)

11. EBCDIC
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The EBCDIC is an 8 bit code primarily used
by IBM and IBM compatible computer
system.
It allows a large variety of printable special
characters and non-printable control
characters.
All 256 (28) bit combinations have not yet
been assigned characters.

12. ASCII
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These codes are of two types: ASCII-7 and
ASCII-8.
 ASCII-7 is a 7 bit code that allows 128 (27)
different characters.
 ASCII-8 is a 8 bit code that allows 256 (28)
different character.

13. Unicode
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It is 16 bit code to represent different
65000+ characters/ symbols of different
languages.
Unicode can represent many of the world’s
languages.

14. Logic Gates
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OR Gate
AND Gate
NOT Gate
NOR Gate
NAND Gate
XOR Gate
XNOR Gate

15. Logic Gates
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OR Gate:
Example: out= A+B

16. AND Gate
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Example: Y= A.B

17. NOT Gate
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Example: out = 𝑨

18. NOR Gate
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Example: out = A+B

19. NAND Gate
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Example: out = 𝑨. 𝑩

20. XOR Gate
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21. XNOR Gate
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22. Logic Expression with Logic Gate
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Y = AB + CD
F = 𝑿 𝒀 Z + 𝑿 Y Z + X 𝒀
F = (A+B).(C+D)
Y = (A+B).( 𝑨 + 𝑩)
F =( 𝑿 𝒀 + 𝑿 Z + 𝑿𝒀𝒁)⨁( 𝑿 𝒀 Z + 𝑿 Y Z + X 𝒀)

23. Thank You
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