This document discusses the design of a floating point multiplier. It begins by explaining the representation of floating point numbers with sign, exponent, and significand. It then describes why floating point is used over fixed point for its wider range of values and greater precision over integers. The key steps for multiplying floating point numbers are described as adding the exponents and multiplying the significands, while XORing the signs. Block diagrams and techniques for partial product generation and accumulation are presented, including radix-4 Booth multiplication and use of carry save adders and ripple carry adders. Finally, floating point formats for single, double, and quadruple precision are shown along with using the divide and conquer technique for higher precision multiplication.

1. DESIGN OF FLOATING POINT
MULTIPLIER

2. Representation of Floating Point
Number
Decimal Number: -7.5
1 10000001 11100000000000000000000
Sign Exponent Mantissa(Significand)

3. Why Floating Point???
 It can support a much wider range of values as
compared to fixed point.
 As compared to Integer, Floating Point is more
precised.

4. How to Multiply??
 Adding the exponent of the two numbers then
subtracting the bias from their result.
 Multiplying the significand of the two numbers.
 Calculating the sign by XORing the sign of the two
numbers.

5. Block Diagram of Floating Point
Multiplier

6. SIGNIFICAND MULTIPLICATION
Multiplication of Significand is done in two steps:
1. Partial Product generation
2. Accumulation of generated Partial Products.

7. PARTIAL PRODUCTS GENERATION
Partial Products generation can be done by various
methods, but Radix-4 Booth Multiplication is one of the
best technique
xi xi-1 xi-2 Operation
0 0 0 +0
0 0 1 +A
0 1 0 +A
0 1 1 +2A
1 0 0 -2A
1 0 1 -A
1 1 0 -A
1 1 1 +0

8. ACCUMULATION OF PARTIAL
PRODUCTS
Accumulation of Partial products can be done by various
adders, such as:
1. Ripple Carry Adder (RCA)
2. Carry Select Adder (CSLA)
3. Carry Look Ahead Adder (CLA)
4. Carry Save Adder (CSA)
Carry Save Adder & Ripple Carry Adder are used for
Accumulation.

9. Floating Point Formats
Single precision Double Precision Quadruple
Precision
Computer
Memory
4 bytes (32 bits) 8 bytes (64 bits) 16 bytes (128 bits)
Sign bit 1 1 1
Exponent Width 8 11 15
Significand
Precision
23 52 112

10. Divide & Conquer Technique

11. Divide & Conquer Technique in
Quadruple Precision Multiplication

12. THANK YOU…..