Total Boolean Logic Functions of Two Input System

In this blog post we will be get to know about how many total Boolean logic functions are possible with a single / two input digital system.

Let's start with a single input system as below -

 - The total Boolean functions which can be obtained from Single Input System are as below  - 

Boolean Function	Name of the Boolean Function	Meaning
0	Null	Always 0
1	Identity	Always 1
A	Transfer	Pass Value of A
Bar{A}	NOT	Pass Negated Value of A

                                                    Table #1: Single Input System Boolean Functions

-Hence, total Boolean functions which can be obtained from a Single Input System are 4

- In General : Total Boolean Functions Obtained from an 'N' Input System are 2^{2^{N}}

Now, Let's see what all Boolean Functions can be obtained from a 2 Input System as below-

-Table below captures all the 16 Boolean functions possible for a 2 Input System.

Boolean Function	Name of the Boolean Function	Meaning
0	Null	Always 0
1	Identity	Always 1
A	Transfer	Pass Value of A
B	Transfer	Pass Value of B
Bar{A}	NOT	Pass Negated Value of A
Bar{B}	NOT	Pass Negated Value of B
A*B	AND	1 Only if A and B both are 1
Bar{A*B}	NAND	0 Only if A and B both are 1
A+B	OR	0 Only if A and B both are 0
Bar{A+B}	NOR	1 Only if A and B both are 0
A + Bar{B}	Implication	If B, then A
Bar{A} + B	Implication	If A, Then B
A*Bar{B}]	Inhibition	A but not B
Bar{A}*B	Inhibition	B but not A
A      B	EX-OR	A or B, but not both
Bar{A      B}	EX-NOR	1 if A equals to B

                                       Table #2 : 2 Input System Boolean Functions 

Implication Function : In implication logic, the output will either be driven to a high or would replicate the state of one of the inputs, depending on the value of the other input.

Inputs		Output
A	B	Y
0	0	1
0	1	1
1	0	0
1	1	1

                              Table #3: Implication – A implies B [Bar{A} + B]

Inhibition Function : The inhibition function is the complementary version of implication.

Inputs		Output
A	B	Y
0	0	0
0	1	0
1	0	1
1	1	0

                                     Table #4: Inhibition – A inhibits B [A * Bar{B}]

 

Thank !