计算机组成原理课后题6.20PPT.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,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=0.110 111,，,y=-0.101 110,；,（,2,）,x=-0.010 111,，,y=-0.010 101,；,（,3,）,x=19,，,y=35,；,（,4,）,x=0.110 11,，,y=-0.111 01,。,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 x,0,=0,，,y,0,=1,，,z,0,=x,0,y,0,=0,1=1,x*,y*=0.100 111 100 010,xy,原,=1.,100 111 100 010,x,y=-0.,100 111 100 010,1,原码一位乘：,部分积 乘数,y*0.0 0 0 0 0 0 .1 0 1 1 1,0,+0,1,0.0 0 0 0 0 0 0.1 0 1 1,1,+x*,+0.1 1 0 1 1 1 0.1 1 0 1 1 1,1 0.0 1 1 0 1 1 1 0.1 0 1,1,+x*,+0.1 1 0 1 1 1 1.0 1 0 0 1 0,1 0.1 0 1 0 0 1 0 1 0 .1 0,1,+x*,+0.1 1 0 1 1 1 1.1 0 0 0 0 0,1 0.1 1 0 0 0 0 0 0 1 0.1,0,+0,1 0.0 1 1 0 0 0 0 0 0 1 0.,1,x*,+0.1 1 0 1 1 1 1.0 0 1 1 1 1,1 0.1 0 0 1 1 1 1 0 0 0 1 0,2,2x*=01.101110,，,-x*,补,=-x,补,=1.001001,原码两位乘：,部分积 乘数,Cj 0 0 0.0 0 0 0 0 0 0 0.1 0 1 1,1 0,0 +0 0 1.1 0 1 1 1 0 +2x*0 0 1.1 0 1 1 1 0 0,2 0 0 0.0 1 1 0 1 1 1 0 0 0.1 0,1 1,+1 1 1.0 0 1 0 0 1 +-x*,补,1 1 1.1 0 0 1 0 0 1,2,1 1 1.1 1 1 0 0 1 0 0 1 0 0 0.,1 0,+,1 1 1.0 0 1 0 0 1 +-x*,补,1 1 1.0 0 0 0 1 0,1,2,1 1 1.1 1 0 0 0 0 1 0 0 0 1 0,0 0,.,+0 0 0.1 1 0 1 1 1 +x*0 0 0.1 0 0 1 1 1 1 0 0 0 1 0 0,结果同一位乘，,x,y=-0.,100 111 100 010,3,x,补,x=0.110111y,补,=1.010010-x,补,=1.0010012x,补,=01.101110-2x,补,=10.010010,x,y,补,=1.011 000 011 110 0,xy=-0.100 111 100 010 0,补码一位乘、两位乘运算过程如下：,4,补码一位乘：,部分积 乘数,y,补,y,n+1,0 0.0 0 0 0 0 0 1.0 1 0 0 1,0 0,+0,1 0,0.0 0 0 0 0 0 0 1.0 1 0 0,1 0,+1 1.0 0 1 0 0 1 +-x,补,1 1.0 0 1 0 0 1,1 1 1.1 0 0 1 0 0 1 0 1.0 1 0,0 1,+0 0.1 1 0 1 1 1 +x,补,0 0.0 1 1 0 1 1,1 0 0.0 0 1 1 0 1 1 1 0 1 .0 1,0 0,+0,1 0 0.0 0 0 1 1 0 1 1 1 0 1.0,1 0,+1 1.0 0 1 0 0 1,+-x,补,1 1.0 0 1 1 1 1,1 1 1.1 0 0 1 1 1 1 1 1 1 0 1.,0 1,+0 0.1 1 0 1 1 1 +x,补,0 0.0 1 1 1 1 0,1 0 0.0 0 1 1 1 1 0 1 1 1 1 0,1 .0,+,1 1.0 0 1 0 0 1 +-x,补,1 1.0 1 1 0 0 0 0 1 1 1 1 0,0,清,0,5,补码两位乘：,部分积 乘数,y,n+1,0 0 0.0 0 0 0 0 0 1 1.0 1 0 0,1 0 0,+1 1 0.0 1 0 0 1 0 +-2x,补,1 1 0.0 1 0 0 1 0,2 1 1 1.1 0 0 1 0 0 1 0 1 1.0 1,0 0 1,+0 0 0.1 1 0 1 1 1 +x,补,0 0 0.0 1 1 0 1 1,2,0 0 0.0 0 0 1 1 0 1 1 1 0 1 1.,0 1 0,+,0 0 0.1 1 0 1 1 1 +x,补,0 0 0.1 1 1 1 0 1,2,0 0 0.0 0 1 1 1 1 0 1 1 1 1 0,1 1 .0,+1 1 1.0 0 1 0 0 1 +-x,补,1 1 1.0 1 1 0 0 0 0 1 1 1 1 0 0 0.,结果同补码一位乘，,x,y=-0.,100 111 100 010 00,6,（,2,）,x=-0.010111,，,y=-0.010101 x,原,=1.010111,，,y,原,=1.010101 x*=0.010111,，,y*=0.010101,-x*,补,=1.101001,，,2x*=0.101110 -2x*,补,=1.010010,x,0,=1,，,y,0,=1,，,z,0,=x,0,y,0,=1,1=0 x,补1.101001,，,y,补,=1.101011 -x,补,=0.010111,，,2x,补,=1.010010 -2x,补,=0.101110,x*,y*=0.000 111 100 011,xy,原,=0.,000 111 100 011 xy,补,=0.,000 111 100 011 0,x,y=0.,000 111 100 011,运算过程如下：,7,原码一位乘：,部分积 乘数,y*0.0 0 0 0 0 0 .0 1 0 1 0,1,+x*,+,0.0 1 0 1 1 1 0.0 1 0 1 1 1,1 0.0 0 1 0 1 1 1,.0 1 0 1,0,+0,1 0.0 0 0 1 0 1 1 1,.0 1 0,1,+x*,+0.0 1 0 1 1 1 0.0 1 1 1 0 0,1 0.0 0 1 1 1 0 0 1 1 .0 1,0,+0,1 0.0 0 0 1 1 1 0 0 1 1.0,1,+x*,+0.,0 1 0 1 1 1,0.0 1 1 1 1 0,1 0.0 0 1 1 1 1 0 0 0 1 1.0 +0,1 0.0 0 0 1 1 1 1 0 0 0 1 1,8,原码两位乘：,部分积 乘数,y*Cj 0 0 0.0 0 0 0 0 0 0 0.0 1 0 1,0 1,0 +0 0 0.0 1 0 1 1 1 +x*0 0 0.0 1 0 1 1 1 0,2 0 0 0.0 0 0 1 0 1 1 1 0 0.0 1,0 1,+,0 0 0.0 1 0 1 1 1,+x*0 0 0.0 1 1 1 0 0 0,2 0 0 0.0 0 0 1 1 1 0,0 1 1 0 0.,0 1,+0 0 0.0 1 0 1 1 1,+x*0 0 0.0 1 1 1 1 0,0,2 0 0 0.0 0 0 1 1 1 1 0 0,0 1 1,0 0,.,+0,结果同一位乘，,x,y=0.,000 111 100 011,9,补码一位乘：,部分积 乘数,y,补,y,n+1,0 0.0 0 0 0 0 0 1.1 0 1 0 1,1 0,+0 0.0 1 0 1 1 1 +-x,补,0 0.0 1 0 1 1 1,1,0 0.0 0 1 0 1 1 1 1.1 0 1 0,1 1,+0,1,0 0.0 0 0 1 0 1 1 1 1.1 0 1,0 1,+1 1.1 0 1 0 0 1 +x,补,1 1.1 0 1 1 1 0,1 1 1.1 1 0 1 1 1 0,1 1 1 .1 0,1 0,+,0 0.0 1 0 1 1 1 +-x,补,0 0.0 0 1 1 1 0,1 0 0.0 0 0 1 1 1 0 0,1 1 1.1,0 1,+1 1.1 0 1 0 0 1 +x,补,1 1.1 1 0 0 0 0,1 1 1.1 1 1 0 0 0 0 0 0,1 1 1.,1 0,+,0 0.0 1 0 1 1 1 +-x,补,0 0.0 0 1 1 1 1,1,0 0.0 0 0 1 1 1 1,0 0 0,1 1,1 .1,+0,10,补码两位乘：,部分积 乘数,y,n+1,0 0 0.0 0 0 0 0 0 1 1.1 0 1 0,1 1 0,+0 0 0.0 1 0 1 1 1 +-x,补,0 0 0.0 1 0 1 1 1,2,0 0 0.0 0 0 1 0 1 1 1 1 1.1 0,1 0 1,+0 0 0.0 1 0 1 1 1 +-x,补,0 0 0.0 1 1 1 0 0,2 0 0 0.0 0 0 1 1 1 0 0,1 1 1 1.,1 0 1,+,0 0 0.0 1 0 1 1 1 +-x,补,0 0 0.0 1 1 1 1 0,2 0 0 0.0 0 0 1 1 1 1 0 0 0,1 1,1 1,.,1,清,0,+0,结果同补码一位乘，,x,y=0.,000 111 100 011 00,11,（,3,）,x=19,，,y=35 x=,（,10 011,）,2,，,y=,（,100 011,）,2,x*=x,原,=,x,补,=,0,，,010 011 y*=y,原,=,y,补,=,0,，,100 011,-x*,补,=-x,补,=1,，,101 101 2x*=2x,补,=0,，100 110 -2x*,补,=-2x,补,=1,，,011 010,x,0,=0,，,y,0,=0,，,z,0,=x,0,y,0,=0,0=0,x,y=x*,y*=xy,原,=,xy,补,=,0,，,001 010 011 001,运算过程如下：,12,原码一位乘：,部分积 乘数,y*0,，,0 0 0 0 0 0 1 0 0 0 1,1,+x*,+,0,，,0 1 0 0 1 1 0,，,0 1 0 0 1 1,1,0,，,0 0 1 0 0 1 1,1,0 0 0,1,+x*,+,0,，,0 1 0 0 1 1 0,，,0 1 1 1 0 0,1,0,，,0 0 1 1 1 0 0 11,0 0,0,+0,1,0,，,0 0 0 1 1 1 0 0 1,1,0,0,+0,1,0,，,0 0 0 0 1 1 1 0 0 1,1,0,+0,1,0,，,0 0 0 0 0 1 1 1 0 0 1,1,+x*,+0,，,0 1 0 0 1 1 0,，,0 1 0 1 0 0,1,0,，,0 0 1 0 1 0 0,1 1 0 0 1,13,原码两位乘：,部分积 乘数,y*Cj 0 0 0,，,0 0 0 0 0 0 0 0,，,1 0 0 0,1 1,0 +1 1 1,，,1 0 1 1 0 1 +-x*,补,1 1 1,，,1 0 1 1 0 1 1,2 1 1 1,，,1 1 1 0 1 1 0 1 0 0,，,1 0,0 0,+,0 0 0,，,0 1 0 0 1 1,+x*0 0 0,，,0 0 1 1 1 0 0,2 0 0 0,，,0 0 0 0 1 1 1,0 0 1 0 0,，,1 0,+0 0 0,，,1 0 0 1 1 0,+2x*0 0 0,，,1 0 1 0 0 1,0,2 0 0 0,，,0 0 1 0 1 0 0 1,1,0 0 1,0 0,，,+0,结果同一位乘，,x,y=0,，,001 010 011 001,14,补码一位乘：,部分积 乘数,y,补,y,n+1,0 0,，,0 0 0 0 0 0 0,，,1 0 0 0 1,1 0,+1 1,，,1 0 1 1 0 1 +-x,补,1 1,，,1 0 1 1 0 1,1,1 1,，,1 1 0 1 1 0 1 0,，,1 0 0 0,1 1,+0,1,1 1,，,1 1 1 0 1 1 0 1 0,，,1 0 0,0 1,+0 0,，,0 1 0 0 1 1 +x,补,0 0,，,0 0 1 1 1 0,1 0 0,，,0 0 0 1 1 1 0,0 1 0,，,1 0,0 0,+0,1 0 0,，,0 0 0 0 1 1 1 0,0 1 0,，,1,0 0,+0,1 0 0,，,0 0 0 0 0 1 1 1 0,0 1 0,，,1 0,+,1 1,，,1 0 1 1 0 1 +-x,补,1 1,，,1 0 1 1 1 0,1,1 1,，,1 1 0 1 1 1 0,1 1 0,0 1,0,，,1,+0 0,，,0 1 0 0 1 1 +x,补,0 0,，,0 0 1 0 1 0,0,1 1 0,0 1,0,15,补码两位乘：,部分积 乘数,y,n+1,0 0 0,，,0 0 0 0 0 0 0 0,，,1 0 0 0,1 1 0,+1 1 1,，,1 0 1 1 0 1 +-x,补,1 1 1,，,1 0 1 1 0 1,2,1 1 1,，,1 1 1 0 1 1 0 1 0 0,，,1 0,0 0 1,+0 0 0,，,0 1 0 0 1 1 +x,补,0 0 0,，,0 0 1 1 1 0,2 0 0 0,，,0 0 0 0 1 1 1 0,0 1 0 0,，,1 0 0,+,1 1 1,，,0 1 1 0 1 0 +-2x,补,1 1 1,，,0 1 1 1 0 1,2 1 1 1,，,1 1 0 1 1 1 0 1 1 0,0 1,0 0,，,1,+0 0 0,，,0 1 0 0 1 1 +0 0 0 0,，,0 0 1 0 1 0,0 1 1 0,0 1,0 0,结果同补码一位乘，,x,y=0.,000 111 100 011 00,16,（,4,）,x=0.110 11,，,y=-0.111 01 x*=x,原,=,x,补,=,0.110 11 y,原,=1.111 01,，,y*=0.111 01,y,补,=1.000 11,-x*,补,=-x,补,=1.001 01 2x*=2x,补,=01.101 10 -2x*,补,=-2x,补,=10.010 10,x,0,=0,，,y,0,=1,，,z,0,=x,0,y,0,=0,1=1,x*,y*=0.110 000 111 1,xy,原,=1.,110 000 111 1 xy,补,=1.,001 111 000 10,x,y=-0.,110 000 111 1,运算过程如下：,17,原码一位乘：,部分积 乘数,y*,0.0 0 0 0 0 .1 1 1 0,1,+x*,+0.1 1 0 1 1 0.1 1 0 1 1,1 0.0 1 1 0 1 1,.1 1 1,0,+0,1 0.0 0 1 1 0 1 1,.1 1,1,+x*,+0.1 1 0 1 1 1.0 0 0 0 1,1 0.1 0 0 0 0 1 1 1 .1,1,+,x*,+0.,1 1 0 1 1,1.0 1 0 1 1,1 0.1 0 1 0 1 1 1 1 1.1 +,x*,+0.,1 1 0 1 1 1.1 0 0 0 0,1 0.1 1 0 0 0 0 1 1 1 1,18,原码两位乘：,部分积 乘数,y*Cj 0 0 0.0 0 0 0 0 0.1 1 1,0 1,0 +0 0 01 1 0 1 1 +x*0 0 0.1 1 0 1 1 0,2 0 0 0.0 0 1 1 0 1 1 0.1,1 1,+,1 1 1.0 0 1 0 1,+-x*,补,1 1 1.0 1 0 1 1 1,2 1 1 1.1 1 0 1 0,1 1 1 1 .,0 1,+0 0 1.1 0 1 1 0,+2x*0 0 1.1 0 0 0 0,0,1 0 0 0.1 1 0 0 0 0 1,1 1 1,0.,+0,结果同一位乘，,x,y=-0.,110 000 111 1,19,补码一位乘：,部分积 乘数,y,补,y,n+1,0 0.0 0 0 0 0 1.0 0 0 1,1 0,+1 1.0 0 1 0 1 +-x,补,1 1.0 0 1 0 1,1,1 1.1 0 0 1 0 1 1.0 0 0,1 1,+0,1,1 1.1 1 0 0 1 0 1 1.0 0,0 1,+0 0.1 1 0 1 1 +x,补,0 0.1 0 1 0 0,1 0 0.0 1 0 1 0 0,0 1 1 .0,0 0,+0,1 0 0.0 0 1 0 1 0 0,0 1 1.,0 0,+0,1 0 0.0 0 0 1 0 1 0 0,0 1,1.0,+,1 1.0 0 1 0 1 +-x,补,1 1.0 0 1 1 1,1 0 0,0 1,0,清,0,20,补码两位乘：,部分积 乘数,y,n+1,0 0 0.0 0 0 0 0 1.0 0 0,1 1 0,+1 1 1.0 0 1 0 1 +-x,补,1 1 1.0 0 1 0 1,2,1 1 1.1 1 0 0 1 0 1 1.0,0 0 1,+0 0 0.1 1 0 1 1 +x,补,0 0 0.1 0 1 0 0,2 0 0 0.0 0 1 0 1 0,0 0 1,1.0 0,+,1 1 0.0 1 0 1 0 +-2x,补,1 1 0.0 1 1 1 1,1 1 1 1.0 0 1 1 1 1 0 0,0 1,0.,清,0,结果同补码一位乘，,x,y=-0.,110 000 111 10,21,