115023

: : 115023

115023

1.

a) (10100111.1)2 -> (167.5)10

10100111.1 = 27 + 2

5 + 2

2 + 2

1 + 2

-1 = 167.5

b) (1011 0111 1111)2 = (B7F)16

11 7 5

2.

f1=x1x2+x1x3x4+x1x2x3+x1x2x4 f2=x1x2+x1x3+x1x3x4+x1x2x3x4

115023

f3=x2x4+x2x3+x2x3x4 f4 =x3

PLA:

115023

3.

I0=x1x2x2x3=0 I1=x1x2x2x3=0

I2=x1x2x2x3=x1x2x3 I3=x1x2x2x3=x1x2x3

A1=I3 XOR x4

A2 =(A1+I2+I1) = A1I2I1 = A1I2*1=A1I2

f=A2+I0 = A2+0 = A2 = A1I2 = (I3 XOR x4)(x1x2x3) =

= (I3x4+I3x4)(x1+x2+x3)=(x1x2x3x4+(x1+x2+x3)x4)(x1+x2+x3)=

= (x1x2x3x4+x1x4+x2x4+x3x4)(x1+x2+x3) =

= x1x2x3x4+ x1x4+x1x2x4+x1x3x4+x1x2x4+x2x4+x2x3x4+

+x1x3x4+x2x3x4 = x1x2x3x4 + x1x4(1+x3+x3+x2)+x2x4(1+x3+x3)=

= x1x2x3x4 + x1x4+ x2x4 =

= x1x2x3x4 + x1x2x4+ x1x2x4+ x1x2x4+ x1x2x4 =

= x1x2x3x4 +x1x2x3x4+x1x2x3x4+ x1x2x3x4+ x1x2x3x4+

+x1x2x3x4+x1x2x3x4 ;

115023

4.

Q1Q2Q3 X D1 D2 D3

0 1 X=0 X=1 X=0 X=1 X=0 X=1

A->000 000,0 001,1 0 0 0 0 0 1

B->001 000,0 010,0 0 0 0 1 0 0

C->010 011,0 010,0 0 0 1 1 1 0

D->011 000,0 100,0 0 1 0 0 0 0

E->100 000,0 101,1 0 1 0 0 0 1

F->101 011,1 001,1 0 0 1 0 1 1

0 1

A A,0 B,0

B A,0 C,0

C D,0 C,0

D A,0 E,0

E A,0 F,1

F D,1 B,1

115023

x Q1Q2Q3 Q1+Q2

+Q3

+,Z D1 D2 D3

0 000 000.0 0 0 0

0 001 000.0 0 0 0

0 010 011.0 0 1 1

0 011 000.0 0 0 0

0 100 000.0 0 0 0

0 101 011.1 0 1 1

0 110 b b b b

0 111 b b b b

1 000 001.1 0 0 1

1 001 010.0 0 1 0

1 010 010.0 0 1 0

1 011 100.0 1 0 0

1 100 101.1 1 0 1

1 101 001.1 0 0 1

1 110 b b b b

1 111 b b b b

D1 = xQ2Q3 + xQ1Q3 D2 = xQ1Q2Q3 + xQ1Q3 + Q2Q3

D3 = xQ2Q3 + xQ2Q3 + Q1Q3 Z= xQ2Q3 + Q1Q3

115023

115023

5.

Q5 Q4 Q3 Q2 Q1

0 0 0 0 0 0

1 0 0 0 0 1

2 0 0 0 1 1

3 0 0 1 1 1

4 0 1 1 1 1

5 1 1 1 1 1

6 1 1 1 1 0

7 1 1 1 0 0

8 1 1 0 0 0

9 1 0 0 0 0

0 0 0 0 0 0