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1. DATA
REPRESENTATION
Presented by
Anil Pokhrel
Bsccsit 3 semester
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2. Contents
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 Data types
 Number system
 Complements
 Floating point representation
 Fixed point representation
 Overflow
 Error detection code

3. Data Types
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 The data types found in digital registers or
memory is classified as one of the
following types:
 Numbers used in arithmetic computation
 Letters of alphabets used in data processing
 Other symbols used for specific purpose

4. Number system
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 The data types found in digital
registers or memory is classified as
one of the following types:
Numbers used in arithmetic computation
Letters of alphabets used in data
processing
Other symbols used for specific purpose

5. Representation of Decimal
numbers
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- By converting into binary :
Arithmetic and logical calculation
becomes easy. Negative numbers can be
represented easily.
- By using BCD codes :
This approach is useful in the systems
where there is much input/output than
arithmetic and logical calculation

6. Complements
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8. Floating Point Representation
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9. 9
 Mantissa
 Signed fixed point number, either an integer or
a fractional number
 Exponent
 Designates the position of the decimal point
 Decimal Value
 N = m * r e
 Where m is mantissa
 r is base
 e is exponent

10. Example
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11. Fixed Point Representation
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 Sign bit placed in the leftmost position of the
number determine if the number is positive or
negative. It is 1 for negative and o for positive.
 The fixed point assumes one of the following
case:
 Binary point in the extreme left to make stored
number fraction .
 Binary point in extreme right to make the stored
number an integer

12. Representation of Negative
numbers
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 -Signed magnitude representation
 - Signed 1’s complement representation
 - Signed 2’s complement representation

13. Signed magnitude
representation
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 Complement only the sign bit
 e.g.
 +9 ==> 0 001001
 -9 ==> 1 001001

14. Signed 1’s and 2’s complement
representation
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 Signed 1’s complement representation
 Complement all the bits including sign bit
 e.g.
 +9 ==> 0 001001
 -9 ==> 1 110110
 Signed 2’s complement representation
 Take the 2's complement of the number, including its
sign bit.
 e.g.
 +9 ==> 0 001001
 -9 ==> 1 110111

15. Overflow Detection
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 If we add two n bit numbers, result may be a
number with n+1 bit which cannot be stored in
n-bit register
 When two unsigned numbers are added, an
overflow is detected from the end carry out of
the most significant position

16. Case Unsigned numbers
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19. ERROR DETECTING CODES
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 Binary information transmitted is subjected to
noise which alters certain bits.
 An error detection code is a binary code that
detects digital errors during
transmission(cannot correct).
 If the errors occur at random, the message is
transmitted again.
 If the error is too often, the system is checked
for mal function.
 Most common error detection code is the
parity bit

20.  Even Parity
 One bit is attached
to the information so
that the total number
of 1 bits is an even
number
 Message Parity
 1011001 0
 1010010 1
 Odd Parity
 One bit is attached
to the information so
that the total number
of 1 bits is an odd
number
 Message Parity
 1011001 1
 1010010 0
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21. Parity generator
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22. Reffernces
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 M. Moris Mano – computer system and
computer architecture
 https://www.docsity.com/en/data-
representation-computer-architecture-lecture-
slides/202477

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