1. Overview Introduction Data representation Fixed Point Representation
Data Representation Lecture 5
Overview
Introduction
Data representation
Fixed Point Representation
Integer Representation
Floating Point Representation
Normalization
CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT

2. Floating Point Representation
Data Representation Lecture 5
Floating Point Representation
The location of the fractional point is not fixed to a certain location
The range of the represent able numbers is wide
F = EM
mn ekek e0 mn-1mn-2 … m0 . m-1 … m-m
sign exponent mantissa
- Mantissa
Signed fixed point number, either an integer or a fractional number
- Exponent
Designates the position of the radix point
Decimal Value
V(F) = V(M) * RV(E)
V stands for Value
M: Mantissa
E: Exponent
R: Radix
CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT

3. Floating Point Representation
Data Representation Lecture 5
Floating Point Representation
Example 04
sign
mantissa
exponent
==> x 10+04
Example
A binary number in 16-bit floating point number representation
(6-bit exponent and 10-bit fractional mantissa)
Note:
In Floating Point Number representation, only Mantissa(M) and Exponent(E) are explicitly represented. The Radix(R) and the position of the Radix Point are implied.
Exponent
Sign or
Mantissa
CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT

4. Floating Point Representation-Normalization
Data Representation Lecture 5
Floating Point Representation-Normalization
A Floating Point number is said to be normalized if the most significant digit of the mantissa is nonzero
E.g. Binary number is not normalized
CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT