# 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.
3 of 30
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.
4 of 30
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
7 of 30
What is a tautology
if and only if A and B ( when A and B are equivalent)
8 of 30
Name two ways in proving a tautology
by creating truth table of ab or by comparing table a to table b
9 of 30
Write the equation for replacement
G (three lines) G[E/F]
10 of 30
how many combinations can a truth table have
2^n, where n = number of variables
11 of 30
What is the clue for the associative law
Order of brackets does not matter
12 of 30
Associative Laws
(A | B) | C = A | (B |C) AND (A & B) & C = A & (B & C)
13 of 30
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
18 of 30
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
30 of 30

## Other cards in this set

### Card 2

#### Front

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

True ->False

### Card 3

#### Front

What are short circuits?

### Card 4

#### Front

How do short circuits work?

### Card 5

#### Front

Example of short circuit A&&B