Logic Gates.

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Presentation transcript:

Logic Gates

AND In order for current to flow, both switches must be closed Logic notation AB = C (Sometimes AB = C) A B C 1

OR Current flows if either switch is closed Logic notation A + B = C A 1

Properties of AND and OR Commutation A + B = B + A A  B = B  A Same as Same as

Properties of AND and OR Associative Property A + (B + C) = (A + B) + C A  (B  C) = (A  B)  C =

Properties of AND and OR Distributive Property A + B  C = (A + B)  (A + C) A + B  C A B C Q 1

Inversion (NOT) A Q 1 Logic:

Exclusive OR (XOR) Either A or B, but not both This is sometimes called the inequality detector, because the result will be 0 when the inputs are the same and 1 when they are different. The truth table is the same as for S on Binary Addition. S = A  B A B S 1

Getting the XOR A B S 1 Two ways of getting S = 1

Circuit for XOR

NAND (NOT AND) A B Q 1

NOR (NOT OR) A B Q 1

Exclusive NOR A B Q 1 Equality Detector

Summary for Truth Tables Summary for all 2-input gates Inputs Output of each gate A B AND NAND OR NOR XOR XNOR 1

Summary for Logic Gates

MORE LOGIC GATES Try and work out the truth tables for these gates. The rule will help you. AND OR A B Q XOR A B Q A Q B RULE: Q = 1 if A AND B =1 RULE: Q = 1 if A OR B =1 Q = 1 if A OR B =1, but NOT both A B Q 1 A B Q 1 A B Q 1 NOT NAND A B Q NOR A B Q A Q RULE: Q = 0 if A AND B =1 RULE: Q = 0 if A OR B =1 RULE: Q = 0 if A =1 A B Q 1 A B Q 1 A Q 1

LOGIC GATES AND OR XOR NOT NAND NOR A B Q A B Q A Q B RULE: Q = 1 if A AND B =1 RULE: Q = 1 if A OR B =1 Q = 1 if A OR B =1, but NOT both A B Q 1 A B Q 1 A B Q 1 NOT NAND A B Q NOR A B Q A Q RULE: Q = 0 if A AND B =1 RULE: Q = 0 if A OR B =1 RULE: Q = 0 if A =1 A B Q 1 A B Q 1 A Q 1