Logic Design Fundamentals Flashcards
Positive Logic
Low Voltage corresponds to Logic 0
High Voltage corresponds to Logic 1
AND Gate
00 : 0
01 : 0
10 : 0
11 : 1
OR Gate
00 : 0
01 : 1
10 : 1
11 : 1
NOT Gate (Inverter)
1 : 0
0 : 1
XOR Gate
00 : 0
01 : 1
10 : 1
11 : 0
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?
X’Y’Cin + X’YCin’ + XY’Cin’ + XYCin
001 + 010 + 100 + 111
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?
X’YCin + XY’Cin + XYCin’ + XYCin
011 + 101 + 110 + 111
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?
m(1,2,4,7)
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?
m(3,5,6,7)
What form is this?
ABC + A’BC + AB’C + ABC’
Sum of Products
-ORing minterms together
What form is this?
A+B+C)(A’+B+C)(A+B’+C)(A+B+C’
Product of Sums
-ANDing maxterms
X + 0 =
X + 1 =
X * 1 =
X * 0 =
X + 0 = X
X +1 = 1
X * 1 = X
X * 0 = 0
X + X =
X * X =
Idempotent Law:
X + X = X
X * X = X
(X’)’ =
Double Inversion of X =
Involution Law:
(X’)’ = X
X + X’ =
X * X’ =
Complementarity Law:
X + X’ = 1
X * X’ = 0
X + Y =
XY =
Commutative Law:
X + Y = Y + X
XY = YX
(X+Y) + Z =
(XY)Z =
Associative Law:
(X+Y) + Z = X + (Y+Z) = X + Y + Z
(XY)Z = X(YZ) = XYZ
X(Y + Z) =
X + YZ =
Distributive Law:
X(Y + Z) = XY + XZ
X + YZ = (X+Y) (X+Z)
XY + XY’ =
X + XY =
(X +Y’)Y =
Simplification Theorem:
XY + XY’ = X
X + XY = X
(X +Y’)Y = XY
(X + Y)( X+Y’) =
X(X+Y) =
XY’ + Y =
(X + Y)( X+Y’) = X
X(X+Y) = X
XY’ + Y = X + Y
