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Level 29

A2 1.4.3 - Boolean Algebra


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de Morgan's first law
¬(A V B) = (¬A) Λ (¬B)
de Morgan's second law
¬(A Λ B) = (¬A) V (¬B)
0
X Λ 0 =
X
X Λ X =
X
X Λ 1 =
0
X Λ ¬X =
X
X V 0 =
X
X V X =
1
X V 1 =
1
X V ¬X =
double negation law
¬¬X = X
commutative law (and)
A Λ B = B Λ A
commutative law (or)
A V B = B V A
associative law (and)
(A Λ B) Λ C = A Λ (B Λ C)
associative law (or)
(A V B) V C = A V (B V C)
distributive law (and)
A Λ (B V C) = ( A Λ B ) V (A Λ C)
distributive law (or)
A V (B Λ C) = ( A V B ) Λ (A V C)
absorption law (and)
A Λ (A V B) = A
absorption law (or)
A V (A Λ B) = A
half adder
a logic circuit consisting of an XOR and AND gate that takes two inputs and outputs the result of the addition of the inputs
sum in half adder
= A ⊻ B
carry bit in half adder
= A ∧ B
full adder
a logic circuit connecting two half adders with an OR gate to add two inputs together in addition to a carry bit
sum in full adder
= A ⊻ B ⊻ C
carry bit in full adder
= (A ∧ B) ∨ (C ∧ (A ⊻ B))
n bits
n full adders can be connected in order to perform addition on two binary numbers with ...
flip flop
an elemental sequential logic circuit that can store one bit and flip between two states
oscillator
a sequential circuit that changes state at regular time intervals
d-type flip flop
a positive edge-triggered flip flop, meaning that it can only change its output at the point of a clock pulse and will store the state of a bit, thus it can be used as a memory cell
register memories
these are constructed by connecting a series of flip flops in a row and are used for the intermediate storage needed during arithmetic operations