Схемотехника

Проектирование устройства, осуществляющего перемножение двух четырехразрядных чисел


                                  Часть 2.

                                                        х1х2х3х4
                                                        х5х6х7х8

                               (х1х8)(х2х8)(х3х8)(х4х8)
                     (х1х7)(х2х7)(х3х7)(х4х7)
           (х1х6)(х2х6)(х3х6)(х4х6)
 (х1х5)(х2х5)(х3х5)(х4х5)


|х3х8            |Х4х7            |Y7              |Р1              |
|0               |0               |0               |0               |
|0               |1               |1               |0               |
|1               |0               |1               |0               |
|1               |1               |0               |1               |


Y7=(а+b)+(a+b);  a=x3x8; b=x4x7   P1=ab

|a         |b         |c         |P1        |P2        |Y6        |P2’       |
|0         |0         |0         |0         |0         |0         |0         |
|0         |0         |0         |1         |0         |1         |0         |
|0         |0         |1         |0         |0         |1         |0         |
|0         |0         |1         |1         |1         |0         |0         |
|0         |1         |0         |0         |0         |1         |0         |
|0         |1         |0         |1         |1         |0         |0         |
|0         |1         |1         |0         |1         |0         |0         |
|0         |1         |1         |1         |1         |1         |0         |
|1         |0         |0         |0         |0         |1         |0         |
|1         |0         |0         |1         |1         |0         |0         |
|1         |0         |1         |0         |1         |0         |0         |
|1         |0         |1         |1         |1         |1         |0         |
|1         |1         |0         |0         |1         |0         |0         |
|1         |1         |0         |1         |1         |1         |0         |
|1         |1         |1         |0         |1         |1         |0         |
|1         |1         |1         |1         |0         |0         |1         |

После упрощения Y6=(cp1+cp1)(ab+ab)+(cp1+cp1)(ab+ab)

P2=a(bp1+bp1)+p1(bc+bc)+abc      a=x2x8;b=x3x7;c=x4x6
P2’=abcp1

|a      |b      |c      |d      |P2     |P3     |Y5     |P3’    |
|0      |0      |0      |0      |0      |0      |0      |0      |
|0      |0      |0      |0      |1      |0      |1      |0      |
|0      |0      |0      |1      |0      |0      |1      |0      |
|0      |0      |0      |1      |1      |1      |0      |0      |
|0      |0      |1      |0      |0      |0      |1      |0      |
|0      |0      |1      |0      |1      |1      |0      |0      |
|0      |0      |1      |1      |0      |1      |0      |0      |
|0      |0      |1      |1      |1      |1      |1      |0      |
|0      |1      |0      |0      |0      |0      |1      |0      |
|0      |1      |0      |0      |1      |1      |0      |0      |
|0      |1      |0      |1      |0      |1      |0      |0      |
|0      |1      |0      |1      |1      |1      |1      |0      |
|0      |1      |1      |0      |0      |1      |0      |0      |
|0      |1      |1      |0      |1      |1      |1      |0      |
|0      |1      |1      |1      |0      |1      |1      |0      |
|0      |1      |1      |1      |1      |0      |0      |1      |
|1      |0      |0      |0      |0      |0      |1      |0      |
|1      |0      |0      |0      |1      |1      |0      |0      |
|1      |0      |0      |1      |0      |1      |0      |0      |
|1      |0      |0      |1      |1      |1      |1      |0      |
|1      |0      |1      |0      |0      |1      |0      |0      |
|1      |0      |1      |0      |1      |1      |1      |0      |
|1      |0      |1      |1      |0      |1      |1      |0      |
|1      |0      |1      |1      |1      |0      |0      |1      |
|1      |1      |0      |0      |0      |1      |0      |0      |
|1      |1      |0      |0      |1      |1      |1      |0      |
|1      |1      |0      |1      |0      |1      |1      |0      |
|1      |1      |0      |1      |1      |0      |0      |1      |
|1      |1      |1      |0      |0      |1      |1      |0      |
|1      |1      |1      |0      |1      |0      |0      |1      |
|1      |1      |1      |1      |0      |0      |0      |1      |
|1      |1      |1      |1      |1      |0      |1      |1      |

После упрощения:

Y5=(dp2+dp2)(a(bc+bc)+a(bc+bc))+(dp2+dp2)c(ab+ab)

P3=bd(ac+ac)+cp2(ac+ab)+ab(cp2+cp2)+dp2(ab+ab)+abcp2

P3=bd(ac+ac)+cp2(ad+ad)+(ab+ab)(dp2+cp2)+abcp2 a=x1x8;b=x2x7;c=x3x6;d=x4x5

|A      |b      |c      |P2’    |P3     |P4     |Y4     |P4’    |
|0      |0      |0      |0      |0      |0      |0      |0      |
|0      |0      |0      |0      |1      |0      |1      |0      |
|0      |0      |0      |1      |0      |0      |1      |0      |
|0      |0      |0      |1      |1      |1      |0      |0      |
|0      |0      |1      |0      |0      |0      |1      |0      |
|0      |0      |1      |0      |1      |1      |0      |0      |
|0      |0      |1      |1      |0      |1      |0      |0      |
|0      |0      |1      |1      |1      |1      |1      |0      |
|0      |1      |0      |0      |0      |0      |1      |0      |
|0      |1      |0      |0      |1      |1      |0      |0      |
|0      |1      |0      |1      |0      |1      |0      |0      |
|0      |1      |0      |1      |1      |1      |1      |0      |
|0      |1      |1      |0      |0      |1      |0      |0      |
|0      |1      |1      |0      |1      |1      |1      |0      |
|0      |1      |1      |1      |0      |1      |1      |0      |
|0      |1      |1      |1      |1      |0      |0      |1      |
|1      |0      |0      |0      |0      |0      |1      |0      |
|1      |0      |0      |0      |1      |1      |0      |0      |
|1      |0      |0      |1      |0      |1      |0      |0      |
|1      |0      |0      |1      |1      |1      |1      |0      |
|1      |0      |1      |0      |0      |1      |0      |0      |
|1      |0      |1      |0      |1      |1      |1      |0      |
|1      |0      |1      |1      |0      |1      |1      |0      |
|1      |0      |1      |1      |1      |0      |0      |1      |
|1      |1      |0      |0      |0      |1      |0      |0      |
|1      |1      |0      |0      |1      |1      |1      |0      |
|1      |1      |0      |1      |0      |1      |1      |0      |
|1      |1      |0      |1      |1      |0      |0      |1      |
|1      |1      |1      |0      |0      |1      |1      |0      |
|1      |1      |1      |0      |1      |0      |0      |1      |
|1      |1      |1      |1      |0      |0      |0      |1      |
|1      |1      |1      |1      |1      |0      |1      |1      |


После упрощения:

Y4=(p2’p3+p2’p3)(abc+abc+abc)+ap2’p3(bc+bc)+abcp2’+abcp2’p3

P4=(p2’+p3)b(ac+ac)+abc(p2’+p3)+abp(p2’+c)+abc(p2’+p3)+abcp2’p3

P4’=p2’p3(bc+ac+ab)+abc(p2’+p3)     a=x1x7;b=x2x6;c=x3x5


|A       |b       |P3’     |P4      |P5      |Y3      |
|0       |0       |0       |0       |0       |0       |
|0       |0       |0       |1       |0       |1       |
|0       |0       |1       |0       |0       |1       |
|0       |0       |1       |1       |1       |0       |
|0       |1       |0       |0       |0       |1       |
|0       |1       |0       |1       |1       |0       |
|0       |1       |1       |0       |1       |0       |
|0       |1       |1       |1       |1       |1       |
|1       |0       |0       |0       |0       |1       |
|1       |0       |0       |1       |1       |0       |
|1       |0       |1       |0       |1       |0       |
|1       |0       |1       |1       |1       |1       |
|1       |1       |0       |0       |1       |0       |
|1       |1       |0       |1       |1       |1       |
|1       |1       |1       |0       |1       |1       |
|1       |1       |1       |1       |0       |0       |


После упрощения:

Y3=(ab+ab)(p3’p4+p3’p4)+(ab+ab)(p3’p4+p3’p4)

P5=p4b(a+p3’)+b(ap3’+p3’p4+ap4)

a=x1x6;b=x2x5

|A           |P4’         |P5          |P6          |Y2          |
|0           |0           |0           |0           |0           |
|0           |0           |1           |0           |1           |
|0           |1           |0           |0           |1           |
|0           |1           |1           |1           |0           |
|1           |0           |0           |0           |1           |
|1           |0           |1           |1           |0           |
|1           |1           |0           |1           |0           |
|1           |1           |1           |1           |1           |

После упрощений:

Y2=p4’(ap5+ap5)+p4’(ap5+ap5)

P6= p4’p5+a(p4’+p5) a=x1x5



Y1=P6= p4’p5+a(p4’+p5)
Y8=x4x8





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