Floating Point Multiplication.pptx

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 0.5 ten and -0.4375 ten 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 Binary Representation 0.5 10 = 0.1 2 0.4375 10 = 0.0111 2 +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 0.5 ten and -0.4375 ten 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 0.5 ten and -0.4375 ten in binary using the floating point Multiplication algorithm

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

7. Example Step 4 : Rounding 1.110000 x 2 -3 G R S Rounding Action Truncate 1 Truncate 1 Truncate 1 1 Truncate 1 Round to Even 1 1 Round Up 1 1 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 0.5 ten and -0.4375 ten in binary using the floating point Multiplication algorithm 1.110 x 2 -3

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