Introduction to DLD

AND Gate Using NOR Gate

An AND logic Gate can be made using NOR logic gates. As we know, NOR is a universal logic gate, meaning it can be used to build other basic logic gates such as OR, AND, NOT, NAND, XOR, and XNOR. Implementing an AND gate using a NOR gate is useful when you need an AND logic circuit but only have NOR gates available; an AND logic gate is unavailable.

AND Gate Using NAND Gate - AND gate not available, only NOR available

AND logic gate and a NOR logic gate, both are different in terms of output. So we have to implement NOR 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 inputs is 0 (LOW). AND Logic Gate Truth Table and its symbols are given below

AND Gate Using NAND Gate - AND gate 2 inputs

NOR Logic Gate

The NOR gate is a fundamental logic gate commonly used in digital logic design to perform the NOT-OR operation. It produces a HIGH output (1) only when all its inputs are LOW (0). If any input is HIGH (1), the output will be LOW (0).

AND Gate Using NAND Gate - NOR Gate 2 inputs

If we want to construct an AND gate which contains a various number of inputs, then various numbers of NOR gates are required to implement this process. Let’s discuss various cases

AND Gate Using NOR Gate: 2-Input

If we want to construct a 2-input OR logic gate using NOR gates, then 3 NOR gates are required to implement this process.

  • First NOR gate: Takes “A” as an input, and the output is A’
  • Second NOR gate: Takes “B” as an input, and the output is B’
  • Third NOR gate: It takes the outputs of the first two NOR gates which is A’ , B’ as input and produces the result A.B by using De Morgan’s law.

The following diagram explains the process

AND Gate Using NAND Gate - 2 inputs

AND Gate Using NOR Gate: 3-Input

If we want to construct a 2-input OR logic gate using NOR gates, then 4 NOR gates are required to implement this process.

  • First NOR gate: Takes “A” as an input, and the output is A’
  • Second NOR gate: Takes “B” as an input, and the output is B’
  • Third NOR gate: Takes “C” as an input, and the output is C’
  • 4th NOR gate: It takes the output of the first three NOR gates which is A’ , B’ , C’ as a input and produce the the result A.B.C by using De Morgan’s law.

The following diagram explains the process

AND Gate Using NAND Gate - 3 inputs

AND Gate Using NOR Gate: 4-Input

If we want to construct a 2-input OR logic gate using NOR gates, then 5 NOR gates are required to implement this process.

  • First NOR gate: Takes “A” as an input, and the output is A’
  • Second NOR gate: Takes “B” as an input, and the output is B’
  • Third NOR gate: Takes “C” as an input, and the output is C’
  • 4th NOR gate: Takes “D” as an input, and the output is D’
  • 5th NOR gate: It takes the output of the first three NOR gates which is A’ , B’ , C’ , D’ as a input and produces the result A.B.C.D by using De Morgan’s law.

The following diagram explains the process

AND Gate Using NAND Gate - 4 inputs