Introduction to DLD

AND Gate Using NAND Gate

An AND 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 OR, AND, NOT, XOR, and XNOR. Implementing an AND gate using NAND gates is useful when you need an AND logic circuit but only have NAND gates available.

OR Gate Using NAND Gate - Need to Produce AND Gate Result

AND logic gate and the NAND logic gate, both are different in terms of output. So we have to implement a NAND gate in such a way that its results are exactly similar to an AND logic gate.

AND Logic Gate

An AND logic gate produces the output 1 (High) when all inputs are 1 (High). Output will becomes  0 (LOW) only the case when any input is 0 (LOW). AND logic gate truth table and its symbols are given below

AND Logic Gate - Truth table and symbol

NAND Logic Gate

A NAND logic gate produces the output 0 (LOW) only in the case when all inputs are 1 (HIGH). For all other input combinations, the output is 1 (HIGH). NAND logic gate truth table and its symbols are given below

NAND Logic Gate - Truth table and symbol

If we want to construct an AND gate with multiple inputs, we need different numbers of NAND gates to implement this. Let’s discuss various cases.

2-input AND Logic Gate Using NAND Gate

If we want to construct a 2-input AND gate using NAND gates, we need 2 NAND gates to implement this process. Let’s explain it in 2 simple steps.

Step 01: Consider 1-NAND Logic Gates

The first NAND gate is configured to take two inputs. This setup effectively inverts the input due to the nature of the NAND operation. When the input is 0, it is transformed into 1, and vice versa.

AND Gate Using NAND Gate - 2 inputs step 1

In the above diagram

  • The first NAND logic Gate takes A and B as input and produces (A.B)’

AND Logic Gate Using NAND Gate – Truth Table

The truth table of Step 01 (2-input AND logic gates) is given below

AND Gate Using NAND Gate - Step 1 Truth Table using 2-Inputs

Step 02: Take 2nd NAND Logic Gates

2nd NAND logic gate takes the output of the first NAND gate as an input and produces the final AND output, as shown in the following diagram

AND Gate Using NAND Gate - 2 inputs step 2

According to Using the Double Complement Law, the 2nd NAND gate produces the final AND gate output.

  • Output : (A · B)′’ = A . B

AND Logic Gate Using NAND Gate – Truth Table

The truth table of Step 02 (2-input AND logic gate) is given below

AND Gate Using NAND Gate - Step 2 Truth Table using 2-Inputs

3-input AND Logic Gate Using NAND Gate

Important: We are going to solve this case with 3 NAND gates, but it can be done using only 2 NAND gates by taking first NAND gate, which takes all 3 inputs, and the 2nd NAND gate produces the final result.

If we want to construct a 3-input AND gate using NAND gates, we can use 3 or more NAND gates to implement this process. Let’s explain it in 2 simple steps.

Step 01: Consider 2-NAND Logic Gates

The first NAND gate is configured to take a single three inputs (A,B,C). This setup effectively inverts the input due to the nature of the NAND operation. When the input is 0, it is transformed into 1, and vice versa.

The following diagram explains the process

AND Gate Using NAND Gate - 3 inputs step 1

In the above diagram

  • First NAND logic Gate takes A and B as input and produces (A · B. C)’

AND Logic Gate Using NAND Gate – Truth Table

The truth table of Step 01 (3-input AND logic gates) is given below

AND Gate Using NAND Gate - Step 1 Truth Table using 3-Inputs

Step 02: Take 2nd NAND Logic Gates

2nd NAND logic gate takes the output of the first NAND gate as an input and produces the final AND output, as shown in the following diagram

AND Gate Using NAND Gate - 3 inputs step 2

According to Using the Double Complement Law, the 3rd NAND gate produces the final AND gate output.

  • Output : (A · B . C)′’ = A . B .  C

AND Logic Gate Using NAND Gate – Truth Table

The truth table of Step 02 (3-input AND logic gate) is given below

AND Gate Using NAND Gate - Step 2 Truth Table using 3-Inputs

4-input OR Logic Gate Using NAND Gate

If we want to construct a 4-input AND gate using NAND gates, we need 2 NAND gates to implement this process. Let’s explain it in 2 simple steps.

Step 01: Consider 1-NAND Logic Gates

The first NAND gate is configured to all four inputs. This setup effectively inverts the input due to the nature of the NAND operation. When the input is 0, it is transformed into 1, and vice versa.

AND Gate Using NAND Gate - 4 inputs step 1

In the above diagram

  • The first NAND logic Gate Takes A, B, C, D as input and produces (A · B. C .D)’

AND Logic Gate Using NAND Gate – Truth Table

The truth table of Step 01 (4-Input AND logic gates) is given below

AND Gate Using NAND Gate - Step 1 Truth Table using 4-Inputs

Step 02: Take 2nd NAND Logic Gates

2nd NAND logic gate takes the output of the first NAND gate as an input and produces the final AND output, as shown in the following diagram

AND Gate Using NAND Gate - 4 inputs step 2

According to Using the Double Complement Law, the 2nd NAND gate produces the final AND gate output.

  • Output : (A · B · C · D)′’ = A · B . C . D

AND Logic Gate Using NAND Gate – Truth Table

The truth table of Step 02 (4-input AND logic gate) is given below

AND Gate Using NAND Gate - Step 2 Truth Table using 4-Inputs