This document provides an overview of topics to be covered in CS304PC, a course on Computer Organization and Architecture. It summarizes the textbook and references used in the course. The topics to be covered in Session 18 include data types, complements, fixed point and floating point representations. Floating point representation and normalization are explained. Other topics that will be discussed include Gray code, excess-3 code, error detection codes such as parity bits, and their use in detecting errors during data transmission.

1. CS304PC:Computer Organization
and Architecture (R18 II(I sem))
Department of computer science and engineering
(AI/ML)
Session 18
by
Asst.Prof.M.Gokilavani
VITS
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2. TEXTBOOK:
• 1. Computer System Architecture – M. Moris Mano, Third Edition,
Pearson/PHI.
REFERENCES:
• Computer Organization – Car Hamacher, Zvonks Vranesic, Safea
Zaky, Vth Edition, McGraw Hill.
• Computer Organization and Architecture – William Stallings Sixth
Edition, Pearson/PHI.
• Structured Computer Organization – Andrew S. Tanenbaum, 4th
Edition, PHI/Pearson.
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3. Unit III
Data Representation: Data types ,Complements, fixed point
Representations, Floating point representation.
Computer Arithmetic: Addition and subtraction,
multiplication Algorithms, Division Algorithms, Floating-point
Arithmetic operations, Decimal Arithmetic unit, Decimal
Arithmetic operations.
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4. Topics covered in session 18
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• Data types
• Complements
• Fixed point Representations
• Floating point representations

5. Floating Point representation
• The floating-point representation of a number has two parts
• The first part represents a signed, fixed-point number – the mantissa
• The second part designates the position of the binary point – the
exponent.
• For Example, the decimal number +6132.789 is represented in
floating point with a fraction and an exponent as follows:
Equivalent to +0.6132789 x 10+4
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6. Floating Point representation
• A floating-point number is always interpreted to represent
• Example: the binary number +1001.11 (with 8-bit fraction and 6-bit
exponent)
• Fraction: 01001110
• Exponent: 000100
• Equivalent to +(.1001110)2 x 2+4
• A floating-point number is said to be normalized if the most significant
digit of the mantissa is nonzero
• The decimal number 350 is normalized, 00350 is not
• The 8-bit number 00011010 is not normalized
• Normalize it by fraction = 11010000 and exponent = -3
• Normalized numbers provide the maximum possible precision for the
floating-point number
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7. Other Binary Codes
• Digital systems can process data in discrete form only
• Continuous, or analog, information is converted into digital form by
means of an analog-to-digital converter.
• Gray code
• Excess-3
• Excess-3 gray
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8. Gray code
• The reflected binary or Gray code, is sometimes used for the
converted digital data.
• The Gray code changes by only one bit as it sequences from one
number to the next.
• Gray code counters are sometimes used to provide the timing
sequences that control the operations in a digital system.
• Binary codes for decimal digits require a minimum of four bits.
• Other codes besides BCD exist to represent decimal digits.
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10. Excess-3 and Excess-3 gray
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11. Questions
1.
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12. Error Detection Codes
• Transmitted binary information is subject to noise that could change
bits 1 to 0 and vice versa.
• An error detection code is a binary code that detects digital errors
during transmission.
• The detected errors cannot be corrected, but can prompt the data to be
retransmitted.
• The most common error detection code used is the parity bit.
• A parity bit is an extra bit included with a binary message to make the
total number of 1’s either odd or even .
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14. • The P(odd) bit is chosen to make the sum of 1’s in all four bits odd
• The even-parity scheme has the disadvantage of having a bit
combination of all 0’s .
• Procedure during transmission:
• At the sending end, the message is applied to a parity generator.
• The message, including the parity bit, is transmitted.
• At the receiving end, all the incoming bits are applied to a
parity checker.
• Any odd number of errors are detected.
• Parity generators and checkers are constructed with XOR gates (odd
function).
• An odd function generates 1 iff an odd number if input variables are 1
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16. Topics to be covered in next session 19
• Addition and Subtraction algorithm
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Thank you!!!