Logic gates and logic circuits

Logic gates

• Electronic circuits in computers, many memories 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.
• The checking of the output from a logic gate or logic circuit can be done using a truth table.

NOT gate

Description

• The output, X, is 1 if the input A is NOT 1

How to write this

• X = NOT A (logic notation)
• $X=\bar{A}$ (Boolean algebra)

Truth table

Input	Output
A	X
0	1
1	0

AND gate

Description

• The output, X, is 1 if input A is 1 and input B is 1

How to write this

• X = A AND B (logic notation)
• $X=A\cdot B$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	0
0	1	0
1	0	0
1	1	1

OR gate

Description

• The output, X, is 1 if input A is 1 or input B is 1.

How to write this

• X = A OR B (logic notation)

• $X=A+B$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	0
0	1	1
1	0	1
1	1	1

NAND gate

Description

• The output, X, is 1 if input A is NOT 1 or input B is NOT 1.

How to write this

• X = A NAND B (logic notation)

• $X=\overline{A\cdot B}$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	1
0	1	1
1	0	1
1	1	0

NOR gate

Description

• The output, X, is 1 if: input A is NOT 1 and input B is NOT 1

How to write this

• X = A NOR B (logic notation)

• $X=\overline{A+B}$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	1
0	1	0
1	0	0
1	1	0

XOR gate

Description

• The output, X, is 1 if (input A is 1 AND input B is NOT 1) OR (input A is NOT 1 AND input B is 1)

How to write this

• X = A XOR B (logic notation)
• $X=(A\cdot \bar{B})+(\bar{A}\cdot B)$ (Boolean algebra)

(Note: this is sometimes written as: $(A+B)\cdot \overline{(A\cdot B)}$)

Truth table

Input	Input	Output
A	B	X
0	0	0
0	1	1
1	0	1
1	1	0

Logic circuits 1

• Produce a truth table for the following logic circuit

Hardware

Complete the truth table for the logic circuit.

A	B	C	X
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

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Logic circuits 2

• A safety system uses three inputs to a logic circuit. An alarm, X, sounds if input A represents ON and input B represents OFF, or if input B represents ON and input C represents OFF.
• Produce a logic circuit and truth table to show the conditions which cause the output X to be 1.

Logic statement

X = 1 if (A = 1 AND B = NOT 1) OR (B = 1 AND C = NOT 1) this equates to A is ON and B is OFF
this equates to B is ON AND C is OFF

Boolean algebra

$X=(A\cdot \bar{B})+(B\cdot \bar{C})$

Hardware

Draw the logic circuit for the logic expression:

X = (A AND B) OR (NOT ((A AND C) AND (B OR C))).

A.

B.

C.

D.

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Logic circuits 3

• A wind turbine has a safety system which uses three inputs to a logic circuit. A certain combination of conditions results in an output, X, from the logic circuit being equal to 1. When the value of X = 1, the wind turbine is shut down.
• The following table shows which parameters are being monitored and form the three inputs to the logic circuit.
• The output, X, will have a value of 1 if any of the following combination of conditions occur:
  • either turbine speed ≤ 1000 rpm and bearing temperature > 80 °C
  • or turbine speed > 1000 rpm and wind velocity > 120 kph
  • or bearing temperature ≤ 80 °C and wind velocity > 120 kph

TIP

1. turbine speed 1000 rpm and bearing temperature > 80 °C logic statement:

   (S = NOT 1 AND T = 1)

2. turbine speed > 1000 rpm and wind velocity > 120 kph logic statement:

   (S = 1 AND W = 1)

3. bearing temperature 80 °C and wind velocity > 120 kph logic statement:

   (T = NOT 1 AND W = 1)

Logic circuits in the real world

AND gate

OR gate

NOT gate

Multi-input logic gates

Multi-input AND gates

Multi-input OR gates