Unlocking the Power of NOR Gates: Implementing Complex Logic Expressions

Unlocking the Power of NOR Gates:

Implementing Complex Logic Expressions

NOR Gate:

This is an OR gate followed by a NOT gate, or a NOT-OR gate. If any of 

the inputs are high, the output of the NOR gate is low. An OR gate with a tiny 

circle on the output serves as the sign. The little circle is a representation 

of inversion.

Why it is considered as Universal Gate?

Table:

A	B	~(A+B)
0	0	1
0	1	0
1	0	0
1	1	0

Diagram:

 

Task 1: Verification of AND Function:

    Observation:

            ·        By giving input ‘0’ and ‘0’ the output was ‘0’.

            ·        By giving input ‘0’ and ‘1’ and output was ‘0’.

            ·        By giving input ‘1’ and ‘0’ and output was ‘0’.

            ·        By giving input ‘1’ and ‘1’ and output was ‘1’

            ·        Above steps verify that it’s an AND gate.

A	B	F=A.B
0	0	0
0	1	0
1	0	0
1	1	1

        

    Observation Table:

A	B	X=~A	Y=~B	X+Y	A.B=~(X+Y)
0	0	1	1	1	0
0	1	1	0	1	0
1	0	0	1	1	0
1	1	0	0	0	1

          ·    Step 1: Take Complement of A and Store in X.

        ·     Step 2: Take Complement of B and Store in Y.

        ·     Step 3: Take AND of X.Y.

        ·    Step 4: Complement of ~(X+Y) gives A.B.

    AND gate using NOR:

Task 2: Verification of OR Function:

    Observation:

            ·                    By giving input ‘0’ and ‘0’ the output was ‘0’.

            ·                    By giving input ‘0’ and ‘1’ and output was ‘1’.

            ·                    By giving input ‘1’ and ‘0’ and output was ‘1’.

            ·                    By giving input ‘1’ and ‘1’ and output was ‘1’

            ·                    Above steps verify that it’s an OR gate.

A	B	F=A+B
0	0	0
0	1	1
1	0	1
1	1	1

    Observation Table:

A	B	A+B	M=~(A+B)	~(M)
0	0	0	1	0
0	1	1	0	1
1	0	1	0	1
1	1	1	0	1

       

    OR gate using NOR:

Task 3: Verification of XOR Function:

    Observation:

            ·        By giving input ‘0’ and ‘0’ the output was ‘0’.

            ·        By giving input ‘0’ and ‘1’ and output was ‘1’.

            ·        By giving input ‘1’ and ‘0’ and output was ‘1’.

            ·        By giving input ‘1’ and ‘1’ and output was ’0’.

            ·        Above steps verify that it’s an XOR gate.

A	B	A⊕B
0	0	0
0	1	1
1	0	1
1	1	0

    Observation Table:

A	B	C=NOR		X=A+C		Y=B+C	~X	~Y	M=~X+~Y
0	0	1		1		1	0	0	0
0	1	0		0		1	1	0	1
1	0	0		1		0	0	1	1
1	1	0		1		1	0	0	0
M=~M			M=~M
1			0
0			1
0			1
1			0

    

    ·       Step 1: Column C store the Values According to NOR operation.

    ·       Step 2: Apply OR operation on A and C, store them in Column X.

    ·        Step 3: Apply OR operation on B and C, store them in Column Y.

    ·        Step 4: Take complement of X and Y.

    ·        Step 5: Again, apply OR operation on Complement of X and Y, store 

                     them in Column M.

    ·        Step 6: Take Complement of M.

    ·        Step 7: Again, Complement of M after that we get XNOR by using 

                     only NOR.

    XOR gate using NOR:

Task 4: Verification of XNOR Function:

    Observation:

            ·        By giving input ‘0’ and ‘0’ the output was ‘1’.

            ·        By giving input ‘0’ and ‘1’ and output was ‘0’.

            ·        By giving input ‘1’ and ‘0’ and output was ‘0’.

            ·        By giving input ‘1’ and ‘1’ and output was ’1’.

            ·        Above steps verify that it’s an XNOR gate.

A	B	~( A⊕B)
0	0	1
0	1	0
1	0	0
1	1	1

    Observation Table:

A	B	C=NOR	X=A+C	Y=B+C	~X	~Y	M=~X+~Y	~M
0	0	1	1	1	0	0	0	1
0	1	0	0	1	1	0	1	0
1	0	0	1	0	0	1	1	0
1	1	0	1	1	0	0	0	1

       

    ·   Step 1: Column C store the Values According to NOR operation.

    ·      Step 2: Apply OR operation on A and C, store them in Column X.

    ·   Step 3: Apply OR operation on B and C, store them in Column Y.

    ·   Step 4: Take complement of X and Y.

    ·   Step 5: Again, apply OR operation on Complement of X and Y, store 

                    them in Column  M.

    ·   Step 6: Take Complement of M after that we get XNOR by using only OR.

    XNOR gate using NOR:

        (How many gates are needed to build a certain gate using NOR are CLICK )