EE 466/586 VLSI Design

1. EE 466/586VLSI Design Partha Pande School of EECS Washington State University pande@eecs.wsu.edu

2. Lecture 23 Arithmetic circuits (Cont’d)

3. The Binary Multiplication

4. The Binary Multiplication

5. Partial-Product Generation • Partial products result from the logical AND of multiplicand X with a multiplier bit Yi • Each row in the partial-product array is either a copy of the multiplicand or a row of zeros. • Partial-product array has many zero rows that have no impact on the result.

6. The Array Multiplier

7. The MxN Array Multiplier— Critical Path Critical Path 1 & 2

8. Carry-Save Multiplier • Multiplication result does not change when the output carry bits are passed diagonally downwards instead of only to the right. • Include an extra adder called a vector-merging adder to generate the final results

9. Carry-Save Multiplier

10. Multiplier Floorplan

11. Wallace-Tree Multiplier

12. Wallace-Tree Multiplier

13. Wallace-Tree Multiplier

14. The Binary Shifter

15. The Barrel Shifter Area Dominated by Wiring

16. The Barrel Shifter • Number of rows equals the word length of the data • Number of columns equals to the maximum shift width • The control wires are routed diagonally through the array

17. Full Datapath

18. Datapath With Control