Outline

• Standard logic gate symbols

• Use logic gates to create logic circuits

• Complete a truth table

• Write logic expression

Introduction

• Electronic circuits in computers, solid state drives and controlling devices are made up of thousands of logic gates

• Logic gates take binary inputs and produce a binary output.

• Several logic gates combined together form a logic circuit and these circuits are designed to carry out a specific function.

Logic gate expressions

• Truth table: Shows all the combinations that can be used as input and output.

• Logic expression: Used to represent the logic of the logic gate.

NOT Logic gate

• It is the simplest logic gate with one input and one output.

• It is used to reverse the input to get the output.

• NOT Logic gate

• Truth table

Questions

• You can withdraw money from an ATM only if you enter the correct PIN AND have sufficient funds in your account.

• In a room, the light is designed to turn off when you press the switch, AND it turns on when the switch is released.

• A security light is set to turn on at night when it gets dark AND off during the day when it is light.

• A security light is set to turn on at night when it gets dark and off during the day when it is light.

AND GATE

• Has two input and one output. Output is 1 when both inputs are 1 Otherwise the output is zero.

• AND Gate diagram

• AND gate truth table

• Z = A AND B (Logic notation)

• Z = A.B (Boolean Notation)

OR GATE

• Has two inputs and one output. The output is one when one of the inputs is one or both inputs are one.

• OR Gate diagram

• OR Gate truth table

• Z = A OR B (Logic notation)

• Z = A + B (Boolean notation)

NAND Gate (NOT AND)

• Has two inputs and one output. Output is 0 when both inputs are 1. Otherwise the output is 0.

• NAND gate diagram

• NAND gate truth table

• Z = NOT (A AND B).

• Z = A.B

NOR Logic Gate (NOT OR)

• Has two inputs and one output.

• The only time the output is 1 is when both inputs are 0.

• NOR gate diagram

• Truth table

• Q = NOT(A OR B)

• Q = A+B

XOR gate

• It is also known as EOR gate. It is known as exclusive OR gate. It has two input and one output.

• The output is one when inputs are different and zero when inputs are the same.

• Diagram

Logic Circuit

Combination of several logic gates that are linked together.

Example 01

• Give the logic expression and truth table for the following logic circuit

Answer

• Y = (A OR B ) AND NOT C

Example 02

• Give the logic expression and truth table for the following logic circuit

Answer

• Q =A OR (NOT B AND C)

Example 03

• Give the logic expression and truth table for the following logic circuit

Answer

• Z = (NOT(P AND Q)) XOR NOT Q) AND R

• A = P AND Q

• B = NOT (P AND Q)

• C = NOT Q

• D = A XOR C

• E = D AND R

Homework

1. Give the logic expression and truth table for the following logic circuit

2. Give the logic expression and truth table for the following logic circuits

Question

• Complete the truth table for this logic circuit.

Answer

Question

• Consider the logic expression:

  Z = (A NAND B) OR NOT (B XOR C)

  Complete the truth table

  from the given logic expression.

Answer

Question

• Consider this logic circuit.

• 
  
  Write a logic expression for this logic circuit.

  Complete the truth table from the given

  logic circuit.