计算机组成原理课后题6.20ppt课件

.,20.用原码一位乘、两位乘和补码一位乘（Booth算法）、两位乘计算xy。（1）x=0.110111，y=-0.101110；（2）x=-0.010111，y=-0.010101；（3）x=19，y=35；（4）x=0.11011，y=-0.11101。解：先将数据转换成所需的机器数，然后计算，最后结果转换成真值。（1）x原=x=0.110111，y原=1.101110 x*=0.110111，y*=0.101110 x0=0，y0=1，z0=x0y0=01=1x*y*=0.100111100010xy原=1.100111100010 xy=-0.100111100010,.,原码一位乘：部分积乘数y*0.000000.101110+010.0000000.10111+x*+0.1101110.11011110.01101110.1011+x*+0.1101111.01001010.101001010.101+x*+0.1101111.10000010.1100000010.10+010.01100000010.1x*+0.1101111.00111110.100111100010,.,2x*=01.101110，-x*补=-x补=1.001001原码两位乘：部分积乘数Cj000.00000000.1011100+001.101110+2x*001.10111002000.0110111000.1011+111.001001+-x*补111.10010012111.111001001000.10+111.001001+-x*补111.00001012111.11000010001000.+000.110111+x*000.1001111000100结果同一位乘，xy=-0.100111100010,.,x补=x=0.110111y补=1.010010-x补=1.0010012x补=01.101110-2x补=10.010010xy补=1.0110000111100 xy=-0.1001111000100补码一位乘、两位乘运算过程如下：,.,补码一位乘：部分积乘数y补yn+100.0000001.0100100+0100.00000001.010010+11.001001+-x补11.001001111.100100101.01001+00.110111+x补00.011011100.0011011101.0100+0100.00011011101.010+11.001001+-x补11.001111111.100111111101.01+00.110111+x补00.011110100.0011110111101.0+11.001001+-x补11.0110000111100清0,.,补码两位乘：部分积乘数yn+1000.00000011.0100100+110.010010+-2x补110.0100102111.1001001011.01001+000.110111+x补000.0110112000.000110111011.010+000.110111+x补000.1111012000.00111101111011.0+111.001001+-x补111.01100001111000.结果同补码一位乘，xy=-0.10011110001000,.,（2）x=-0.010111，y=-0.010101x原=1.010111，y原=1.010101x*=0.010111，y*=0.010101-x*补=1.101001，2x*=0.101110-2x*补=1.010010 x0=1，y0=1，z0=x0y0=11=0x补=1.101001，y补=1.101011-x补=0.010111，2x补=1.010010-2x补=0.101110 x*y*=0.000111100011xy原=0.000111100011xy补=0.0001111000110 xy=0.000111100011运算过程如下：,.,原码一位乘：部分积乘数y*0.000000.010101+x*+0.0101110.01011110.0010111.01010+010.00010111.0101+x*+0.0101110.01110010.001110011.010+010.0001110011.01+x*+0.0101110.01111010.00111100011.0+010.000111100011,.,原码两位乘：部分积乘数y*Cj000.00000000.0101010+000.010111+x*000.01011102000.0001011100.0101+000.010111+x*000.01110002000.000111001100.01+000.010111+x*000.01111002000.00011110001100.+0结果同一位乘，xy=0.000111100011,.,补码一位乘：部分积乘数y补yn+100.0000001.1010110+00.010111+-x补00.010111100.00101111.101011+0100.000101111.10101+11.101001+x补11.101110111.1101110111.1010+00.010111+-x补00.001110100.00011100111.101+11.101001+x补11.110000111.111000000111.10+00.010111+-x补00.001111100.0001111000111.1+0,.,补码两位乘：部分积乘数yn+1000.00000011.1010110+000.010111+-x补000.0101112000.0001011111.10101+000.010111+-x补000.0111002000.000111001111.101+000.010111+-x补000.0111102000.00011110001111.1清0+0结果同补码一位乘，xy=0.00011110001100,.,（3）x=19，y=35x=（10011）2，y=（100011）2x*=x原=x补=0，010011y*=y原=y补=0，100011-x*补=-x补=1，1011012x*=2x补=0，100110-2x*补=-2x补=1，011010 x0=0，y0=0，z0=x0y0=00=0 xy=x*y*=xy原=xy补=0，001010011001运算过程如下：,.,原码一位乘：部分积乘数y*0，000000100011+x*+0，0100110，01001110，001001110001+x*+0，0100110，01110010，001110011000+010，000111001100+010，000011100110+010，000001110011+x*+0，0100110，01010010，001010011001,.,原码两位乘：部分积乘数y*Cj000，00000000，1000110+111，101101+-x*补111，10110112111，1110110100，1000+000，010011+x*000，00111002000，000011100100，10+000，100110+2x*000，10100102000，00101001100100，+0结果同一位乘，xy=0，001010011001,.,补码一位乘：部分积乘数y补yn+100，0000000，1000110+11，101101+-x补11，101101111，11011010，100011+0111，111011010，10001+00，010011+x补00，001110100，0001110010，1000+0100，00001110010，100+0100，000001110010，10+11，101101+-x补11，101110111，1101110110010，1+00，010011+x补00，0010100110010,.,补码两位乘：部分积乘数yn+1000，00000000，1000110+111，101101+-x补111，1011012111，1110110100，10001+000，010011+x补000，0011102000，000011100100，100+111，011010+-2x补111，0111012111，11011101100100，1+000，010011+0000，00101001100100结果同补码一位乘，xy=0.00011110001100,.,（4）x=0.11011，y=-0.11101x*=x原=x补=0.11011y原=1.11101，y*=0.11101y补=1.00011-x*补=-x补=1.001012x*=2x补=01.10110-2x*补=-2x补=10.01010 x0=0，y0=1，z0=x0y0=01=1x*y*=0.1100001111xy原=1.1100001111xy补=1.00111100010 xy=-0.1100001111运算过程如下：,.,原码一位乘：部分积乘数y*0.00000.11101+x*+0.110110.1101110.011011.1110+010.0011011.111+x*+0.110111.0000110.10000111.11+x*+0.110111.0101110.101011111.1+x*+0.110111.1000010.1100001111,.,原码两位乘：部分积乘数y*Cj000.000000.111010+000.11011+x*000.1101102000.00110110.111+111.00101+-x*补111.0101112111.110101111.01+001.10110+2x*001.1000001000.11000011110.+0结果同一位乘，xy=-0.1100001111,.,补码一位乘：部分积乘数y补yn+100.000001.000110+11.00101+-x补11.00101111.1001011.00011+0111.11001011.0001+00.11011+x补00.10100100.010100011.000+0100.0010100011.00+0100.