# Drive XOR using `either ` NAND gates or NOR gates.

From Digital Basics section we know the equations for XOR and NAND gates. The equations are also shown below.

Lets follow steps below for conversion.
• XOR equation = A'B+ AB'
• NAND equation = A' + B'
• NOR equation = A' B'
• Truth-tables are discussed next.
• #### Table below lists truth tables of `NAND`, `NOR` and `XOR`.

Input A Input B NAND NOR XOR
0 0 1 1 0
0 1 1 0 1
1 0 1 0 1
1 1 0 0 0

First Lets drive XOR gate using only NAND gates.

LTE - 4G Wireless Technology

Digital fundamentals.

Interview Questions.

Lets reformat the XOR equation.
Step 1 :- A'B + AB' = [(A+B')' + (A'+B)'] using theorems T7, T8 & T9
Step 2 :- [((A')'+B')' + (A' + (B')')'] using theorems T7, T8 and T9

Step 2 involves Invert of A and invert of B. check circuit for nand to inverter

Above are the steps to drive logic for XOR using NAND gates. So the digital logic circuit to drive XOR from NAND is below.

Tutorials `@fullchipdesign.com`

Verilog Tutorial.

LTE Tutorial.

Memory Tutorial.

Second Now lets drive XOR from NOR gates only. The truth tables of XOR and NOR gates arealready discussed above.

Reformat XOR equation by following steps:
XOR is also know as Exclusive OR.
Step 1 :- A'B + AB' +AA’ + BB’ = [(A’+B') (A+B)] using postulate P4 and theorems T7, T8 and T9
Step 2 :- [(AB)'(A’B’)’] using theorems T7, T8 and T9
In step 2, we do invert of A and invert of B.

Check the circuit for NOR to inverter (equivalent of NAND to inverter). So the complete circuit for XOR using NOR gates. Diagram shown next.

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