1. Lecture 4 Multiplier using FPGA 2007/09/28 Prof. C.M. Kyung

2. 2/13 Multiplier using FPGA 1. GOAL is (1) How to design more complex combinational circuit, multiplier, using HDL(Hardware Description Language) for a wide range of logic system. (2) How to analyze and implement the two basic combinational multiplier forms-“array multiplier” and “parallel multiplier”. (3) In particular, how to represent the multiplier through sequential circuit instead of combinational circuit.

3. 3/13 Multiplier using FPGA 2. Multiplication (1) Multiplication for binary numbers 0 x 0 = 0, 0 x 1 = 0, 1 x 0 = 0, 1 x 1 = 1 (2) Shifting & adding operation (partial product & sum of product)

4. 4/13 Multiplier using FPGA 3. Multiplier (1) Array multiplier (2) Parallel multiplier (3) Sequential multiplier

5. 5/13 Multiplier using FPGA 3. Multiplier (1) Array multiplier - Partial product generation and accumulation are merged

6. 6/13 Multiplier using FPGA 3. Multiplier (1) Array multiplier - Partial product generation and accumulation are merged - Classic shift-add multiplication - Adder structure used to combine all the bit products in a multiplier - Logical bit products AND of the bits from each input - Basic structure is simple to implement in FPGAs - Not make efficient use of the logic in many FPGAs - Larger and slower than other implementations - Ripple carry array multiplier (also called row ripple form) - Carry save array multiplier

7. 7/13 Multiplier using FPGA 3. Multiplier (1) Array multiplier Ripple carry array multiplierCarry save array multiplier

8. 8/13 Multiplier using FPGA (2) Parallel multiplier - High-speed multiplication Array Multiplier - Reduce the number of partial products. - Speed up the multiplication. - The gain in speed is obtained at the expense of extra hardware. - Parallel multiplier can be implemented so as to support a high rate of pipelining. Adder tree partial productsmultiplicand result multiplier Adder array

9. 9/13 Multiplier using FPGA (2) Parallel multiplier ☞ Carry save addition Parallel multiplier

10. 10/13 Multiplier using FPGA (3) Sequential multiplier - U = XA - Representation of X : signed-magnitude : 2’s complement : 1’ complement - If X is positive, P(j+1) = (P(j) + x j A) 2 -1 ; j = 0,1,...,n-2, P(0) = 0 U = 2 n-1 P(n-1) accumulated partial products

11. 11/13 Multiplier using FPGA 3. Problem statement (1) Design m*n (unsigned) array multiplier (2) Design k*k (unsigned) parallel multiplier (3) Design k*k (unsigned) sequential multiplier (4) For each multiplier(1~3), Verilog coding & simulation

12. 12/13 Multiplier using FPGA 4. Experiment Requirements (1) Verilog (2) Quartus II

13. 13/13 Multiplier using FPGA 5. References & Contact (1) Textbook - Randy H. Katz, Contemporary Logic Design, (1994) - Charles H. Roth Jr., Fundamentals of Logic Design, (2004) - Israel Koren, Computer Arithmetic Algorithms, (2002) (2) 4 th Week T.A. E-mail bs_choi@kaist.ac.kr arashi@odyssey.kaist.ac.kr (Ext. 8032) (3) Lecture Homepage http://wink.kaist.ac.kr/course/ee306/