Logic Gates

Logic gates are circuits that are used to perform a logical operation in computing and electronics.

A truth table is a diagram that shows all possible logical inputs and their associated outputs.

Two or more inputs where the output is true if all inputs are true

The output is the inverse (opposite) of the input.

Two or more inputs where the output is true if either or both inputs are true

Two or more inputs where the output is true ONLY if one input is exclusively true.

Two or more inputs where the output is false when all inputs are true.

Two or more inputs where the output is true when all inputs are false.

Half adder circuit carries out addition on two numbers (A and B) only

• Full adder circuit carries out addition on two numbers (A and B) and a carry bit. • A series of full adders can be used to add two binary numbers, as the carry bit is available at each stage of the calculation.

A flip flop is an electronic circuit that has two stable states and can be used as a memory device to store one bit of data

A D-type flip flop changes state with each clock pulse, so data is delayed by one clock pulse

1 . A = A 0 . A = 0 A . A = A A .¯A=0 A . B = B . A A . ( B . C ) = (A . B) . C A + (B . C) = (A + B) . (A + C) A . (A + B) = A

0 + A = A 1 + A = 1 A + A = A A+¯A=1 A + B = B + A A + (B + C ) = (A + B) +. C A . (B + C) = (A . B) + (A . C) A + (A . B) = A

A .B=¯(¯A+¯B) and A+ B=¯(¯A.¯B) The laws are straightforward to remember as: 1. Change all AND operators to OR 2. Change all OR operators to AND 3. Change the logical state of each variable, so: A=¯( A) and ¯A= A 4. Change the logical state of the complete expression, so: expression=¯expression (and vice versa)