Floating Point Addition.pptx
- 1. FLOATING POINT ADDITION Mr. C.KARTHIKEYAN, ASSISTANT PROFESSOR, ECE , RMKCET
- 2. FLOATING POINT ADDITION ALGORITHM Step 0: Convert the numbers in Normalized Binary Step 1: Compare the exponents and match it with the larger exponent Step 2: Add the significant bits Step 3: Normalize the sum Step 4: Round the significant bits if there is no overflow
- 3. EXAMPLE 1 Perform addition of the numbers 0.5ten and 0.4375ten in binary using the floating point addition 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. EXAMPLE 1 Perform addition of the numbers 0.5ten and 0.4375ten in binary using the floating point addition algorithm Step 1: Exponent Comparison 1.000 x 2-1 1.110 x 2-2 1.000 x 2-1 1.110 x 2-2 1.000 x 2-1 0.111 x 2-1
- 5. EXAMPLE 1 Perform addition of the numbers 0.5ten and 0.4375ten in binary using the floating point addition algorithm Step 2: Addition 1.000 x 2-1 0.111 x 2-1 1.000 0.111 (+) 1.111 1.111 x 2-1
- 6. EXAMPLE 1 Perform addition of the numbers 0.5ten and 0.4375ten in binary using the floating point addition algorithm Step 3: Normalization 1.111 x 2-1 1.111 x 2-1 (-1)S x 1.F x 2E
- 7. EXAMPLE 1 Perform addition of the numbers 0.5ten and 0.4375ten in binary using the floating point addition algorithm Step 4: Rounding 1.111 x 2-1 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
- 8. EXAMPLE 1 Perform addition of the numbers 0.5ten and 0.4375ten in binary using the floating point addition algorithm Final Answer 1.111 x 2-1 = 0.1111 0.937510
- 9. EXAMPLE 2 Perform addition of the numbers 10.01101 x 21 and 0.00101101 x 22 in binary using the floating point addition algorithm Step 0: Convert to Normalized Binary 10.01101 x 21 0.00101101 x 22 1.001101 x 22 1.01101 x 2-1
- 10. EXAMPLE 2 Perform addition of the numbers 10.01101 x 21 and 0.00101101 x 22 in binary using the floating point addition algorithm 1.001101 x 22 1.01101 x 2-1 Step 1: Exponent Comparison 0.00101101 x 22
- 11. EXAMPLE 2 Perform addition of the numbers 10.01101 x 21 and 0.00101101 x 22 in binary using the floating point addition algorithm 1.001101 x 22 0.00101101 x 22 Step 2: Addition 1.001101 0.00101101 (+) 1.01100001 1.01100001 x 22
- 12. EXAMPLE 2 Perform addition of the numbers 10.01101 x 21 and 0.00101101 x 22 in binary using the floating point addition algorithm Step 3: Normalization 1.01100001 x 22
- 13. EXAMPLE 2 Perform addition of the numbers 10.01101 x 21 and 0.00101101 x 22 in binary using the floating point addition algorithm Step 4: Rounding 1.01100001 x 22 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 1.01100001 x 22 GUARD BIT(G) ROUND BIT(R) STICKY BITS (S) 1.011 x 22