CS2002 - Basics and Logic Laws

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  • Created by: Chris
  • Created on: 10-05-16 00:38
What are boolean variables called?
Propositions
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Which combination of A->B is the only false one
True ->False
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What are short circuits?
The way in which C processes logical conditions.
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How do short circuits work?
The expression is parsed from left to right, it exits (returns true or false) when the first validating argument has been met.
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Example of short circuit A&&B
if A is false, exit and return false, else continue
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Example of short circuit A || B
if A is true, exit and return true, else continue
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Why should Boolean operations be absolutely simplified?
Because unnecessary components waste time in a circuit
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What is a tautology
if and only if A and B ( when A and B are equivalent)
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Name two ways in proving a tautology
by creating truth table of ab or by comparing table a to table b
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Write the equation for replacement
G (three lines) G[E/F]
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how many combinations can a truth table have
2^n, where n = number of variables
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What is the clue for the associative law
Order of brackets does not matter
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Associative Laws
(A | B) | C = A | (B |C) AND (A & B) & C = A & (B & C)
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What is the clue for distribution laws
Expanding brackets
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Distribution Laws
A V (B &C) = AvB & AvC
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What is the clue for the complement laws
rejecting complements
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Complement laws
-0 = 1
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Complement laws
-1 = 0
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Complement laws
-A | A = 1
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Complement laws
-A v A= 0
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De morgans clue
negation = opposite -> opposite signs and negated variables
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De morgan
-(a & b )= -a | -b
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De morgan
-(a | b) = -a & -b
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What the clue is Absorption Law
flip flop operators ABSORB minority variable
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Absorption law
A | (A&B) = A
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Absorption law
A &(A|B) = A
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Zero and unit law
A&0 = 0 A & 1 = A
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Zero and unit law
A | 1 = 1 A | 0 = A
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Idempotence Laws
A & A = A A | A = A
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Commutative Laws
A & B = B & A A | B = B | A
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Other cards in this set

Card 2

Front

Which combination of A->B is the only false one

Back

True ->False

Card 3

Front

What are short circuits?

Back

Preview of the front of card 3

Card 4

Front

How do short circuits work?

Back

Preview of the front of card 4

Card 5

Front

Example of short circuit A&&B

Back

Preview of the front of card 5
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