UNIT 2 - FLOATING POINT *

1. FLOATING POINT
MULTIPLICATION
Mr. C.KARTHIKEYAN,
ASSISTANT PROFESSOR,
ECE , RMKCET

2. FLOATING POINT MULTIPLICATION
ALGORITHM
Step 0: Convert the numbers in Normalized
Binary
Step 1: Add the exponents
Step 2: Multiply the significant bits
Step 3: Normalize the Product
Step 4: Round the significant bits if there is no
overflow
Step 4: Set the Sign of the Product

3. EXAMPLE
Perform addition of the numbers 0.5ten
and -0.4375ten in binary using the
floating point Multiplication algorithm
Step 0: Convert to Normalized Binary
Binary Representation
0.5 x 2 = 1.0 1
0.75 x 2 = 1.50 1
0.50 x 2 = 1.00 1
0.875 x 2 = 1.75 1
0.4375 x 2 = 0.875 0
Binary Representation
0.510 = 0.12
0.437510 = 0.01112
+1.000 x 2-1
-1.110 x 2-2

4. Step 1: Add the Exponent
1.000 x 2-1
-1.110 x 2-2
E = -1
E = -2
E = -1 + -2 = -3
Perform addition of the numbers 0.5ten
and -0.4375ten in binary using the
floating point Multiplication algorithm
EXAMPLE

5. EXAMPLE
Step 2: Multiply the Significant
1.000 x 2-1
-1.110 x 2-2
1.000
1.110 (+)
1.110000 1.110000 x 2-3
Perform addition of the numbers 0.5ten
and -0.4375ten in binary using the
floating point Multiplication algorithm

6. EXAMPLE
Step 3: Normalization
(-1)S x 1.F x 2E
1.110000 x 2-3
1.110000 x 2-3
Perform addition of the numbers 0.5ten
and -0.4375ten in binary using the
floating point Multiplication algorithm

7. EXAMPLE
Step 4: Rounding
1.110000 x 2-3
G R S Rounding Action
0 0 0 Truncate
0 0 1 Truncate
0 1 0 Truncate
0 1 1 Truncate
1 0 0 Round to Even
1 0 1 Round Up
1 1 0 Round Up
1 1 1 Round Up
GUARD
BIT(G)
ROUND
BIT(R)
STICKY BITS
(S)
1.110 x 2-3
Perform addition of the numbers 0.5ten
and -0.4375ten in binary using the
floating point Multiplication algorithm
1.110000 x 2-3

8. EXAMPLE
Step 5: Set the Sign
1.110 x 2-3
Perform addition of the numbers 0.5ten
and -0.4375ten in binary using the
floating point Multiplication algorithm
-1.110 x 2-3