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Multiplier design 2011/10/27. 微處理機 Microprocessor (100 上 ) ARM 內核嵌入式 SOC 原理. 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 Multiplie r. B

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multiplier design 2011 10 27

Multiplier design2011/10/27

微處理機 Microprocessor (100上)

ARM 內核嵌入式SOC原理

one bit multiplier for arm1
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
slide4

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)

A = 0 + 1001

N=1:

MUL=0 A = A + 0

A = 1001 + 0 = 1001

N=2:

MUL=1 A = A + (B LSL 2)

A = 1001 + 100100 = 101101

N=3:

MUL=1 A = A + (B LSL 3)

A = 101101 + 1001000 = 1110101

multiplier design
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
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
slide8

B

A = 10110001 * 11010011

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

slide9
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

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