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AS
A2
Techniques
If you have a good understanding of the logic gate rules, it is possible to work out a simpler solution just by examining the truth table and thinking hard. But this is a rather hit and miss approach and Karnaugh maps and Boolean algebra can be faster and more reliable methods but neither is easy.
Boolean algebra can be used to simplify expressions/circuits to generate a more optimal solution.
Logic Operations
- + means OR
- . means AND
- a line across the top means NOT
- ⊕ means XOR
De Morgan
De Morgan
- A + B = A . B
- A . B = A + B
Gate Behaviour
- AND GATE
- A . 1 = A The gate is open.
- A . 0 = 0 The gate is closed - output low.
- OR GATE
- A + 1 = 1 The gate is closed - output high.
- A + 0 = A The gate is open.
Commutative
- When using AND and OR, it makes no difference if the inputs are swapped.
- A . B = B . A
- A + B = B + A
Associative
- The presence or absence of brackets makes no difference.
- A . (B . C) = (A . B) . C = A . B . C
- A + (B + C) = (A + B) + C = A + B + C
Distributive
- A . (B + C) = A . B + A . C
- (A + B) . (A + C) = A + (B . C)
Identity
- A + A = A
- A . A = A
- A . B + A . B = A
- (A + B) . ( A + B) = A
Redundancy
In all these expressions, one of the items has no effect and can be removed.
- A . (A + B) = A
- A + A . B = A
- 0 . A = 0
- 0 + A = A
- 1 . A = A
- 1 + A = 1
- A . A = 0
- A + A = 1
- A . (A + B) = A . B
- A + A . B = A + B
reviseOmatic V3
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