2. Outline
Introduction
Floating Point Arithmetic
Adder
Multiplier

3. Introduction
Floating point numbers are one possible way of representing real numbers in binary format.
The IEEE 754 standard presents two different formats:
1. Binary interchange format
2. Decimal interchange format.
Where we require this?
Multiplying floating point numbers is a critical requirement for DSP applications involving large dynamic range.
What are the other possible ways?

4. The IEEE Floating-Point Standard
Representation of a real number in floating point format :

5. Flow Chart *

6. Connector has to be here

7. Example Addition of two 5-digit Binary Floating Point numbers:
Step1: Get the number with the larger exponent and subtract it from the smaller exponent.
eL = 24, eS = 22 , so difference = 4 -2 = 2
Let’s say we want to add two 5-digits binary FP numbers:

8. Step 2:
Shift the fraction with the smaller exponent different positions to the right. We can now leave out the exponent since they are both equal. This gives us the following:
We can now leave out the exponent since they are both equal.

9. Step 3:
Add both the fractions
Step 4:
Round-to-nearest-even
1.1110
Result:
24 ×

11. Adder Circuit

12. Flow Chart
Multiplier

13. Block Diagram

14. Example Step 1: Multiply the significands Step 2:
Multiplication of two 5-digit Floating Point numbers:
A = = 40, B = = -7.5
Step 1: Multiply the significands
Step 2:
Place the decimal point:

15. Step 3: Adding the exponents i.e. (E1 + E2 – Bias)
Step 4: Obtain the sign bit and put the result together.

16. Step 5: Normalize the result
(before normalizing)
(normalized)
Result:
(before rounding)
(rounding)