Проектирование устрою, здійснює перемножування двох четырехразрядных чисел

Частина 2.

х1×2×3×4×5×6×7×8.

(х1×8)(х2×8)(х3×8)(х4×8).

(х1×7)(х2×7)(х3×7)(х4×7).

(х1×6)(х2×6)(х3×6)(х4×6) (х1×5)(х2×5)(х3×5)(х4×5).

|х3×8 |Х4×7 |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 |з |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 спрощення 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 |з |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 |з |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 |.

Після 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 |.

Після 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.