微處理機 Microprocessor (100上) ARM 內核嵌入式SOC原理 Multiplier design 2011/10/27
One bit Multiplier for ARM1 Since the 32-bit addition time has a significant effect on the datapath cycle time Maximum clock rate and the processor's performance
One bit Multiplier A B Cin Sum Cout 1
B A = 1 0 0 1 * 1 1 0 1 3 2 1 0 N TURN N=0： MUL=1 A = A + (B LSL 0) Multiplier Shift (B) ALU LSL #N A = A + 0 1 A = A + (B LSL #N)
Multiplier design All ARM processors apart from the first prototype have included hardware support for integer multiplication. Two styles of multiplier have been used Older ARM cores include low-cost multiplication hardware that supports only the 32-bit result multiply and multiply-accumulate instructions Recent ARM cores have high-performance multiplication hardware and support the 64-bit result multiply and multiply-accumulate instructions
Booth algorithm Two bit multiplier This allows all four values of the 2-bit multiplier to be implemented by a simple shift and add or subtract x 3 =[ x (-1) + x 4 ] carrying the x 4 over to the next cycle
modified Booth's algorithm Cin Multiplier Shift (B) ALU Cout 00 LSL #2N A = A + 0 01 A = A + (B LSL #2N) 10 LSL #(2N+1) A = A - (B LSL #(2N+1)) 1 11 A = A - (B LSL #2N) A = A + (B LSL #(2N+1)) A = A – (B LSL #2N)
B A = 10 11 00 01 * 11 01 00 11 3 2 1 0 N TURN N=0： Cin = 0 MUL=11 A = A - (B LSL 0) set Cout = 1 A = 0 + 1111111101001111 N=1： Cin = 1 MUL=00 A = A + (B LSL 2) set Cout = 0 A = 1111111101001111 + 0000001011000100 = 0000001000010011 N=2： Cin = 0 MUL=01 A = A + (B LSL 4) set Cout = 0 A = 1000010011 + 101100010000 = 0000110100100011 N=3： Cin = 0 MUL=11 A = A - (B LSL6) set Cout = 1 A = 110100100011 + 1101001111000000 = 1110000011100011 N=4： Cin = 1 MUL=00 A = A + (B LSL 8) set Cout = 0 A = 1110000011100011 + 1011000100000000 = 1001000111100011 Cin Multiplier Shift (B) ALU Cout 00 LSL #2N A = A + 0 01 A = A + (B LSL #2N) 10 LSL #(2N+1) A = A - (B LSL #(2N+1)) 1 11 A = A - (B LSL #2N) A = A + (B LSL #(2N+1)) A = A – (B LSL #2N)
實習問題 實習一: 使用One bit Multiplier將 10 11 00 01 * 11 01 00 11 的二進制乘法用組合語言寫出。 實習二: 使用Booth‘s algorithm將 10 11 00 01 * 11 01 00 11 的二進制乘法用組合語言寫出。 做完請找助教檢查