DESIGN OF FLOATING POINT MULTIPLIER

Representation of Floating Point NumberDecimal Number: -7.5

1 10000001 11100000000000000000000

Sign Exponent Mantissa(Significand)

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.

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.

Block Diagram of Floating Point Multiplier

SIGNIFICAND MULTIPLICATION

Multiplication of Significand is done in two steps:

1. Partial Product generation2. Accumulation of generated Partial Products.

PARTIAL PRODUCTS GENERATIONPartial 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

ACCUMULATION OF PARTIAL PRODUCTSAccumulation 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.

Floating Point FormatsSingle 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

Divide & Conquer Technique

Divide & Conquer Technique in Quadruple Precision Multiplication

THANK YOU…..