UNIT 2 - FLOATING POINT ADDITION

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