Logic Design Fundamentals

Question 1

Positive Logic

Answer 1

Low Voltage corresponds to Logic 0

High Voltage corresponds to Logic 1

Question 2

AND Gate

Answer 2

00 : 0
01 : 0
10 : 0
11 : 1

Question 3

OR Gate

Answer 3

00 : 0
01 : 1
10 : 1
11 : 1

Question 4

NOT Gate (Inverter)

Answer 4

1 : 0

0 : 1

Question 5

XOR Gate

Answer 5

00 : 0
01 : 1
10 : 1
11 : 0

Question 6

Full Adder:
X,Y,Cin: Cout,Sum
000:  00
001:  01
010:  01
011:  10
100:  01
101:  10
110:  10
111:  11

When does sum = 1?

Answer 6

X’Y’Cin + X’YCin’ + XY’Cin’ + XYCin

001 + 010 + 100 + 111

Question 7

Full Adder:
X,Y,Cin: Cout,Sum
000:  00
001:  01
010:  01
011:  10
100:  01
101:  10
110:  10
111:  11

When does Cout = 1?

Answer 7

X’YCin + XY’Cin + XYCin’ + XYCin

011 + 101 + 110 + 111

Question 8

Minterms:

000 (0) : 00
001 (1) : 01
010 (2) : 01
011 (3) : 10
100 (4) : 01
101 (5) : 10
110 (6) : 10
111 (7) : 11

What is the minterm expansion for S?

Answer 8

m(1,2,4,7)

Question 9

Minterms:

000 (0) : 00
001 (1) : 01
010 (2) : 01
011 (3) : 10
100 (4) : 01
101 (5) : 10
110 (6) : 10
111 (7) : 11

What is the minterm expansion for Cout?

Answer 9

m(3,5,6,7)

Question 10

What form is this?

ABC + A’BC + AB’C + ABC’

Answer 10

Sum of Products

-ORing minterms together

Question 11

What form is this?

A+B+C)(A’+B+C)(A+B’+C)(A+B+C’

Answer 11

Product of Sums

-ANDing maxterms

Question 12

X + 0 =
X + 1 =
X * 1 =
X * 0 =

Answer 12

X + 0 = X
X +1 = 1
X * 1 = X
X * 0 = 0

Question 13

X + X =

X * X =

Answer 13

Idempotent Law:

X + X = X
X * X = X

Question 14

(X’)’ =

Double Inversion of X =

Answer 14

Involution Law:

(X’)’ = X

Question 15

X + X’ =

X * X’ =

Answer 15

Complementarity Law:

X + X’ = 1
X * X’ = 0

Question 16

X + Y =

XY =

Answer 16

Commutative Law:

X + Y = Y + X
XY = YX

Question 17

(X+Y) + Z =

(XY)Z =

Answer 17

Associative Law:

(X+Y) + Z = X + (Y+Z) = X + Y + Z
(XY)Z = X(YZ) = XYZ

Question 18

X(Y + Z) =

X + YZ =

Answer 18

Distributive Law:

X(Y + Z) = XY + XZ
X + YZ = (X+Y) (X+Z)

Question 19

XY + XY’ =
X + XY =
(X +Y’)Y =

Answer 19

Simplification Theorem:

XY + XY’ = X
X + XY = X
(X +Y’)Y = XY

Question 20

(X + Y)( X+Y’) =
X(X+Y) =
XY’ + Y =

Answer 20

(X + Y)( X+Y’) = X
X(X+Y) = X
XY’ + Y = X + Y