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Digital Circuits Exam 2 Cheat Sheet by

Digital Circuits
digital     circuits     exam     boolean

Boolean Algebra Rules

A + 0 = A
A + 1 = 1
A x 0 = 0
A x 1 = A
A + A = A
A + A' = 1
A x A = A
A x A' = 0
A'' = A
A + A'B = A + B
A + AB = A(1+B) = A(1) = A
(A+B)(A+C) = A+BC
A + B = B + A
AB = BA
A+B+C = A+(B+C)
A(B+C) = AB+AC

Laws

Commun­­ative Law
A x B = B x A
 
A + B = B + A
Associ­­ative Law
A x (B x C) = (A x B) x C
 
A + (B + C) = (A + B) +C
Distri­­butive Law
A x (B + C) = A x B + A x C
 
A + B x C = (A+B)(A+C)
 

DeMorgan Rules

(AB)' = A' + B'
(A+B)' = A'B'
Y' = A' x B x C
Y = (A' x B x C)'
Y = A x B' x C'
(A x B x C)' = A' + B' + C'
(A + B + C)' = A' x B' x C'

Theorems

Theorem 1
X + X · Y = X
Theorem 2
X + X' · Y = X + Y
Theorem 3
X · Y + X' · Z + Y · Z = X · Y + X' · Z
Theorem 4
X(X + Y) = X
Theorem 5
X(X' + Y) = X · Y
Theorem 6
(X + Y)(X + Y') = X
Theorem 7
(X + Y)(X' + Z) = X · Z + X' · Y
Theorem 8
(X + Y)(X' + Z)(Y + Z) = (X + Y)(X' + Z)

Binary & Gray Code

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