The document discusses floating point number addition, subtraction, and multiplication in computers. It describes the algorithms for performing floating point addition and subtraction, which include zero checking, significand alignment, addition/subtraction of significands, normalization, and rounding. It also outlines the basic idea and algorithm for floating point multiplication, which involves separating signs, adding exponents, multiplying significands, normalizing, rounding, and checking for overflow. Examples are provided for both addition/subtraction and multiplication. References for further reading on computer architecture and floating point arithmetic are included.

1. TYPE THE SUBJECT NAME HERE
SUBJECT CODE
II IV
CS 8491
Computer Architecture
(Common to CSE & IT)
UNIT NO 2
ARITHMETIC FOR COMPUTERS
2.5 Floating Point - Addition, Subtraction and
Multiplication

2. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
FLOATING POINT NUMBERS - ADDITION AND SUBTRACTION
ALGORITHM :
0. Zero check
- Change the sign of subtrahend
- If either operand is 0, the other is the result
1. Significand alignment: right shift smaller significand until two
exponents are identical.
2. Addition: add significands and report exception if overflow occurs.
3. Normalization
- Shift significand bits to normalize.
- report overflow or underflow if exponent goes out of range.
4. Rounding

3. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
FLOATING POINT NUMBERS - ADDITION AND SUBTRACTION

4. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
FLOATING POINT NUMBERS - ADDITION AND SUBTRACTION

5. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
FLOATING POINT NUMBERS - ADDITION AND SUBTRACTION

6. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
FLOATING POINT NUMBERS - ADDITION AND SUBTRACTION
EXAMPLE:

7. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
FLOATING POINT NUMBERS - MULTIPLICATION
BASIC IDEA :
(m1 x 2e1) x (m2 x 2e2) = (m1 x m2) x 2e1+e2
● Separate signs
● Add exponents
● Multiply significands
● Normalize, round, check overflow
● Replace sign

8. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
FLOATING POINT NUMBERS - MULTIPLICATION
ALGORITHM :

9. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
FLOATING POINT NUMBERS - MULTIPLICATION
EXAMPLE :

10. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
REFERENCES
● David A. Patterson and John L. Hennessy, Computer Organization and Design:
The Hardware/Software Interface, Fifth Edition, Morgan Kaufmann / Elsevier,
2014
● Carl Hamacher, Zvonko Vranesic, Safwat Zaky and Naraig Manjikian, Computer
Organization and Embedded Systems, Sixth Edition, Tata McGraw Hill, 2012
● https://nptel.ac.in/content/storage2/courses/117106114/Week9%20Slides/9.7Fl
oatingPoint.pdf

11. COMPUTER ARCHITECTURE (Common to CSE & IT )
CS 8491
https://www.youtube.com/watch?v=03fhijH6e2w