Digital Logic Gates

Digital systems are constructed using logic gates. Basic Logic gates are AND, OR, NOT, NAND, NOR, EXOR and EXNOR. The basic operations are described below with the aid of truth tables.

AND

A Logic AND Gate is a type of digital logic gate that has an output which is normally at logic level “0” and only goes “HIGH” to a logic level “1” when ALL of its inputs are at logic level “1”. The output state of a “Logic AND Gate” only returns “LOW” again when ANY of its inputs are at a logic level “0”.

The logic or Boolean expression given for a Digital Logic AND Gate is that for Logical Multiplication which is denoted by a single dot or full stop symbol, ( . ) giving us the Boolean expression of:  

 A.B = Q.

 

“If both A and B are true, then Q is true”

Symbol	Truth Table
2-input AND Gate	A	B	Q
	0	0	0
	0	1	0
	1	0	0
	1	1	1
Boolean Expression Q = A.B	Read as A AND B gives Q

OR

A Logic OR Gate or Inclusive-OR gate is a type of digital logic gate that has an output which is normally at logic level “0” and only goes “HIGH” to a logic level “1” when one or more of its inputs are at logic level “1”. The output, Q of a “Logic OR Gate” only returns “LOW” again when ALL of its inputs are at a logic level “0”.

The logic or Boolean expression given for a Digital Logic OR Gate is that for Logical Addition which is denoted by a plus sign, ( + ) giving us the Boolean expression of: 

 A+B = Q.

 “If either A or B is true, then Q is true”

Symbol	Truth Table
2-input OR Gate	A	B	Q
	0	0	0
	0	1	1
	1	0	1
	1	1	1
Boolean Expression Q = A+B	Read as A OR B gives Q

NOT

The digital Logic NOT Gate is the most basic of all the logical gates and is sometimes referred to as an Inverting Buffer or simply a Digital Inverter. It is a single input device which has an output level that is normally at logic level “1” and goes “LOW” to a logic level “0” when its single input is at logic level “1”.

The output from a NOT gate only returns “HIGH” again when its input is at logic level “0” giving us the Boolean expression of:   

A = Q.

“If A is NOT true, then Q is true”

Symbol	Truth Table
Inverter or NOT Gate	A	Q
	0	1
	1	0
Boolean Expression Q = not A or A	Read as inverse of A gives Q

NAND

 

The Logic NAND Gate is a combination of the digital logic AND gate with that of an inverter or NOT gate connected together in series. The NAND (Not – AND) gate has an output that is normally at logic level “1” and only goes “LOW” to logic level “0” when ALL of its inputs are at logic level “1”. The Logic NAND Gate is the reverse or “Complementary” form of the AND gate we have seen previously.

Logic NAND Gate Equivalence

The logic or Boolean expression given for a logic NAND gate is that for Logical Addition, which is the opposite to the AND gate, and which it performs on the complements of the inputs. The Boolean expression for a logic NAND gate is denoted by a single dot or full stop symbol, ( . ) with a line or Overline, ( ‾‾ ) over the expression to signify the NOT or logical negation of the NAND gate giving us the Boolean expression of:   
                                                                                                               ___

A.B = Q.

“If either A or B are NOT true, then Q is true”

Symbol	Truth Table
2-input NAND Gate	A	B	Q
	0	0	1
	0	1	1
	1	0	1
	1	1	0

NOR

The Logic NOR Gate or Inclusive-NOR gate is a combination of the digital logic OR gate with that of an inverter or NOT gate connected together in series. The NOR (Not – OR) gate has an output that is normally at logic level “1” and only goes “LOW” to logic level “0” when ANY of its inputs are at logic level “1”. The Logic NOR Gate is the reverse or “Complementary” form of the OR gate we have seen previously. 

Logic NOR Gate Equivalent

 

The logic or Boolean expression given for a logic NOR gate is that for Logical Multiplication which it performs on the complements of the inputs. The Boolean expression for a logic NOR gate is denoted by a plus sign, ( + ) with a line or Overline, ( ‾‾ ) over the expression to signify the NOT or logical negation of the NOR gate giving us the Boolean expression of:   
                                                                                                              ____

A+B = Q.

 “If both A and B are NOT true, then Q is true”

Symbol	Truth Table
2-input NOR Gate	A	B	Q
	0	0	1
	0	1	0
	1	0	0
	1	1	0

 

EXOR

The two-input “Exclusive-OR” gate is basically a modulo two adder, since it gives the sum of two binary numbers and as a result are more complex in design than other basic types of logic gate. The truth table, logic symbol and implementation of a 2-input Exclusive-OR gate is shown below.

 

Symbol	Truth Table
2-input Ex-OR Gate	A	B	Q
	0	0	0
	0	1	1
	1	0	1
	1	1	0

The truth table above shows that the output of an Exclusive-OR gate ONLY goes “HIGH” when both of its two input terminals are at “DIFFERENT” logic levels with respect to each other. If these two inputs, A and B are both at logic level “1” or both at logic level “0” the output is a “0” making the gate an “odd but not the even gate”. 

EXNOR

The Exclusive-NOR Gate function or Ex-NOR for short, is a digital logic gate that is the reverse or complementary form of the Exclusive-OR function. Basically the “Exclusive-NOR Gate” is a combination of the Exclusive-OR gate and the NOT gate but has a truth table similar to the standard NOR gate in that it has an output that is normally at logic level “1” and goes “LOW” to logic level “0” when ANY of its inputs are at logic level “1”.

Ex-NOR Gate Equivalent

 

Symbol	Truth Table
2-input Ex-NOR Gate	A	B	Q
	0	0	1
	0	1	0
	1	0	0
	1	1	1