NOR Gate Using NAND Gates
A NOR logic Gate can be made using NAND logic gates. As we know, NAND is a universal logic gate, meaning it can be used to build other basic logic gates such as NOT, OR, AND, XOR, and XNOR. Implementing a NOR gate using a NAND gate is useful when you need a NOR logic circuit but only have NAND gates available; a NOR logic gate is unavailable.
NOR Logic Gate
A NOR logic gate produces the output 1 (High) only when all inputs are 0 (Low). The output becomes 0 (Low) when at least one input is 1 (High). The NOR logic gate truth table and its symbols are given below.
NAND Logic Gate
A NAND logic gate produces the output 0 (LOW) only when all inputs are 1 (HIGH). For all other input combinations, the output is 1 (HIGH). The NAND logic gate truth table and its symbols are given below.
2-input NOR Logic Gate Using NAND Gate
If we want to construct a 2-input NOR logic gate using NAND gates, then 4 NAND gates are required to implement this process. Let explain it in simple 3 steps
Step 01: Consider 2 NAND Logic Gates
The first two NAND gates are used to take a single input (i.e., A) at both inputs of each NAND gate. The inputs are inverted because of the NAND operation. If the input is 0, it becomes 1, and vice versa. Both NAND gates produce the complements of A and B because of the Idempotent Law, as shown in the following diagram.
In the above diagram
- The first NAND logic Gate takes A. A as input and produces A ‘. A ‘, which is equal to A’ (Idempotent Law)
- The second NAND logic Gate takes B.B as input and produces B ‘. B ‘, which is equal to B’ (Idempotent Law)
| Note: ≡ is the equivalent symbol. |
Step 02: Take the 3rd NAND logic gate
The third NAND logic gate takes the output of the first two NAND gates as an input and produces the OR (A+B) output by using De Morgan’s Law, as shown in the following diagram
According to De Morgan’s Law, the third NAND gate produces the final OR gate output.
- Output : (A′ · B′)′ = A + B
Step 03: Take the 4th NAND logic gate – Final Result
The 4th NAND logic gate takes the output of the third NAND gate as an input and produces the final result, the NOR (A+B)’ as an output by using De Morgan’s Law, as shown in the following diagram
NOR Logic Gate Using NAND Gate – Truth Table
The truth table of 2-input NOR logic gates is given below
3-input NOR Logic Gate Using NAND Gate
To construct a 3-input NOR logic gate using NAND gates, you need 4 NAND gates. The following diagram explains the entire process
NOR Logic Gate Using NAND Gate – Truth Table
The truth table of a 3-input NOR logic gate is given below
4-input NOR Logic Gate Using NAND Gate
To construct a 4-input NOR logic gate using NAND gates, you need 4 NAND gates. The following diagram explains the entire process
NOR Logic Gate Using NAND Gate – Truth Table
The truth table of a 4-input NOR logic gate is given below
