3.1 已知[x]补和[y]补的值，用补.码加减法计算x+y和x-y（写出结果的二进制表示和十进制表示），并指出结果是否溢出以及溢出的类型(建议采用变形补码计算)。

(1) [x]补=0.11011 , [y]补=0.00011(2) [x]补=0.10111 [y]补=1.00101(3) [x]补=1.01010 [y]补=1.10001(4) [x]补=1.10011 [y]补=0.11001解:(1) [x]补=0.11011 , [y]补=0.00011[－y]补=1.11101[X+Y]补=[x]补+[y]补= 00.11011+ 00.00011__________________00.11110X+Y= +15/16 =+0.1111B[X－Y]补=[x]补+[－y]补=00.11011+11.11101__________________00.11000X－Y= +12/16 =＋3/4=+0.11B检验【X= + 27/ 32Y= +3/32X+Y = +(27+3)/32 =+30/32=0.11110BX－Y = (27－3)/32=+24/32=+3/4=0.11B 】(2) [x]补=0.10111 , [y]补=1.00101[Y]原=1.11011[－y]补=0.11011[X+Y]补=[x]补+[y]补= 00.10111+ 11.00101__________________11.11100X+Y=－0.001B=－1/8[X－Y]补=[x]补+[－y]补= 00.10111+00.11011________________01.10010 (上溢)[X－Y]补=1.10010 (上溢)【修正：X－Y=－0.01110 = －7 / 16+2 = 25 / 16 】检验【X= +23/ 32Y=－27/32X+Y = (23－27)/32 =-4/32=－1/8X－Y = (23+27)/32=+50/32 =25/16 (上溢) 】(3) [x]补=1.01010 , [y]补=1.10001[－y]补=0.01111[X+Y]补=[x]补+[y]补= 11.01010+ 11.10001__________________10.11011X+Y=0.11011B=+27/32[ 修正27/32－2=27－64=－37/32 ][X－Y]补=[x]补+[－y]补= 11.01010+ 00.01111________________11.11001X－Y=－0.00111B=－7/32检验【X= －22/ 32=－11/16Y=－15/32X+Y = (－15－22) /32 =－37/32 (下溢)X－Y = (－22－(－15)) / 32 =－7/32 】(4) [x]补=1.10011 , [y]补=0.11001[ X= －0.01101=－13/ 32Y= +0.11001=25/32X+Y = (－13+25)/32 =12/32=3/8X－Y = (－13－25)/32=－38/32 = -19 / 16 (下溢) ][－y]补=1.00111[X+Y]补=[x]补+[y]补= 11.10011+ 00.11001__________________00.01100X+Y=0.01100B=3/8[X－Y]补=[x]补+[－y]补= 11.10011+ 11.00111________________10.11010 (下溢)[X－Y]补=0.11010 (下溢)【修正：X－Y = 13 / 16 – 2 = －19 / 16 】检验【X= －0.01101=－13/ 32Y= +0.11001=25/32X+Y = (－13+25)/32 =12/32=3/8X－Y = (－13－25)/32=－38/32 = -19 / 16 (下溢) 】3.2 给出x和y的二进制值，用补码加减法计算x+y和x-y（写出结果的二进制表示和十进制表示），并指出结果是否溢出以及溢出的类型(建议采用变形补码什算)、(1) x=0.10111 y=0.11011 (2) x=0.11101 y=0.10011(3) x=0.11011 y=-0.1010 (4) x=-0.11111 y=0.11011(5) x=-0.11011 y=0.1010 (6) x=-0.11010 y=-0.11001(7) x=-1011101 y=+1101101 (8) x=+1110110 y=-1001101 (9) x=+1101110 y=+1010101 (10) x=-1111111 y=-1101101 解：(1)X=0.10111 Y=0.11011[X]补=0.10111[Y]补=0.11011[－Y]补=1.00101[X+Y]补=[X]补+[Y]补= 00.10111+ 00.11011_______________________01.10010 (上溢)X+Y 上溢[X－Y]补=[X]补－[Y]补= 00.10111+ 11.00101_________________________11.11100X-Y=－0.00100=－1/8检验【X=23/32 Y=27/32X+Y=50/32[ 修正：X+Y=-0.0111 =－7 / 16 +2 =25 / 16 ]X－Y=－1/8】(2)X=0.11101 Y=0.10011[X]补=0.11101[Y]补=0.10011[－Y]补=1.01101[X+Y]补=[X]补+[Y]补= 00.11101+ 00.10011_______________________01.10000 (上溢)X+Y 上溢[X－Y]补=[X]补－[Y]补= 00.11101+ 11.01101_________________________00.01010X-Y=0.01010=5/16检验【X=29/32 Y=19/32X+Y=48/32 =3 / 2[ 修正：X+Y = －0.1 = －1 / 2+2 =1.5 ] X－Y=10/32=5 / 16】(3)X=0.11011 Y=－0.1010[X]补=0.11011[Y]补=1.01100[－Y]补=0.10100[X+Y]补=[X]补+[Y]= 00.11011+ 11.01100_______________________00.00111X+Y =7/32[X－Y]补=[X]补－[Y]补= 00.11011+ 00.10100_________________________01.01111X－Y=－0.10001=－17/32 (上溢)[ 修正－17/32+2=47/32 ]检验【X=27/32 Y=－20/32X+Y=7/32X－Y=47/32】(4)X=－0.11111 Y=0.11011[X]补=1.00001[Y]补=0.11011[－Y]补=1.00101[X+Y]补=[X]补+[Y]补= 11.00001+ 00.11011_______________________11.11100X+Y =－0.00100=－1/8[X－Y]补=[X]补－[Y]补= 11.00001+ 11.00101_________________________10.00110 (下溢)X－Y=0.00110=3/16 (下溢)[ 修正6/32－2=58/32 =29/16 ]检验【X=－31/32 Y=27/32X+Y=－4/32 =－1/8X－Y=58/32=29/16】(5)X=－0.11011 Y=0.10100[X]补=1.00101[Y]补=0.10100[－Y]补=1.01100[X+Y]补=[X]补+[Y]补= 11.00101+ 00.10100_______________________11.11011X+Y =－0.00111=－7/32[X－Y]补=[X]补－[Y]补= 11.00101+ 11.01100_________________________10.10001 (下溢)X－Y=17/32 (下溢)[ 修正17/32－2=－47/32 ]检验【X=－27/32 Y=20/32X+Y=－7/32X－Y=－47/32】(6)X=－0.11010 Y=－0.11001[X]补=1.00110[Y]补=1.00111[－Y]补=0.11001[X+Y]补=[X]补+[Y]补= 11.00110+ 11.00111_______________________10.01101X+Y =13/32 (下溢) [ 修正13/32－2=－51/32 ] [X－Y]补=[X]补－[Y]补= 11.00110+ 00.11001_________________________11.11111X－Y=－0.00001= －1/32检验【X=－26/32 Y=－25/32X+Y=－51/32X－Y=－1/32】(7) X=－1011101 Y=+1101101 [X]补=10100011[Y]补=01101101[－Y]补=1.01100[X+Y]补=[X]补+[Y]补= 110100011+ 001101101_______________________000010000X+Y =00010000=16[X－Y]补=[X]补－[Y]补= 110100011+ 110010011_________________________100110110 (下溢) X－Y=54 (下溢)[ 修正54－256=－202 ]检验【X=－93 Y=109X+Y=16X－Y=－202】(8) X=+1110110 Y=－1001101 [X]补=01110110[Y]补=10110011[－Y]补=01001101[X+Y]补=[X]补+[Y]补= 001110110+ 110110011_______________________000101001X+Y =41[X－Y]补=[X]补－[Y]补= 0011101101+ 001001101_________________________011000011 (上溢)X－Y=－61 (上溢)[ 修正－61+256=195 ]检验【X=118 Y=－77X+Y=41X－Y=195】(9)X=+1101110 Y=+1010101[X]补=01101110[Y]补=01010101[－Y]补=10101011[X+Y]补=[X]补+[Y]补= 001101110+001010101_______________________011000011 (上溢)X+Y =－0111101=－61 [ 修正－61+256=195 ] [X－Y]补=[X]补－[Y]补= 001101110+ 110101011_________________________000011001X－Y=25检验【X=110 Y=85X+Y=195X－Y=25】(10) X=－1111111 Y=－1101101[X]补=10000001[Y]补=10010011[－Y]补=01101101[X+Y]补=[X]补+[Y]补= 110000001+ 110010100_______________________100010100 (下溢)X+Y =00010100=20 [ 修正20－256=－236 ] [X－Y]补=[X]补－[Y]补= 110000001+ 001101101_________________________111101110检验【X－Y=－0010010=－18X=－127 Y=－109X+Y=－236X－Y=－18】。