# NOR Calculator

Reviewed by Wojciech Sas, PhD and Steven Wooding
Last updated: Mar 27, 2023

The binary NOR calculator helps you calculate the bitwise NOR output of the given set of numbers, taken 2 at a time. The NOR logic converter is similar to other bit logic calculations such as NAND, XOR, XNOR, etc. In binary, the NOR gate performs the bit operation for each pair of bits in the inputs and calculates the NOR gate output.

## How does a NOR calculator work?

The binary NOR calculator calculates the NOR gate output for a pair of numbers. Each input is converted to binary for the NOR gate since the NOR logic converter performs bit operation in binary form. The output is calculated bit by bit by performing the NOR operation of each pair of input bits. The NOR gate calculates the bit outputs as follows:

• If both input bits are 0, the output bit is 1; and
• If at least one of the input bits is 1, the output bit is 0.

💡 Remember to choose the proper input data type: Binary, octal, or decimal. The calculator will convert them into binary, whichever you select.

For two inputs of N bits each, the NOR gate calculates an N-bit output. For example, if the inputs are 4 bits, the NOR gate calculates a 4-bit output.

In case you're looking for a tool that calculates bitwise AND, OR, or XOR for two numbers, feel free to check out our bitwise calculator!

## What is NOR gate truth table?

A

B

NOR Output

0

0

1

0

1

0

1

0

0

1

1

0

Knowing the NOR truth table, we can see that the NOR gate performs the reverse of the AND gate operation. So from the truth table of NOR, when both inputs are 0, the NOR gate produces 1. For all other combinations of the two input bits, the NOR gate produces 0.

## NOR logic converter example

For example, let's say the two inputs in binary form are:

• A = 1001; and
• B = 0101.

Knowing what the NOR gate truth table is, we can see that the NOR gate calculates a 4-bit output as follows (from left to right):

• Since the first pair of bits has one 1, the first NOR output bit will be 0;
• Since the next pair of bits also have one 1, the second NOR output bit will also be 0;
• Since the third pair of bits are both 0, the third NOR output bit will be 1; and
• Since the last pair of bits are both 1, the final NOR output bit will be 0.

Thus, we see that the NOR gate calculates a 4-bit output of 0010 for the given pair of inputs.

You can also check out the bit shift calculator for more complex binary operations.

Or, if you would like to convert a number from binary to decimal or vice versa, you could check out our binary converter.

## How do I use the NOR gate calculator?

To know what the NOR gate equals for the given set of numbers, we'd do the following:

1. Choose the number of bits in the binary representation. For example, if we choose 8 bits, we can key in decimal numbers between -128 and 127 as inputs.

2. Choose the input data type. You can choose to enter numbers in the binary, decimal, or octal systems.

3. Enter two numbers whose NOR output you need to find. The calculator will evaluate the final NOR output.

4. The binary NOR calculator will give the result in the binary, decimal, and octal systems.

## What are some other bit logic calculators?

Similar to NOR, there are other bit logic converters. These include the basic gates:

• AND gate – Produces 1 only when both inputs are 1, otherwise produces 0;
• OR gate – Produces 0 only when both inputs are 0, otherwise produces 1; and
• NOT gate – Inverts the input bit.

The other logic gates are:

• NAND gate – Produces 0 only when both inputs are 1, otherwise produces 1;
• XOR gate – Produces 1 only when both inputs are different, otherwise produces 0; and
• XNOR gate – Produces 1 only when both inputs are the same, otherwise produces 0.

## FAQ

### Is NOR a universal gate?

Yes, the NOR gate is a universal gate. This is because we can implement any Boolean function with only a combination of NOR gates and no other logical bitwise operators. The NAND gate is another such universal gate using which we can construct any boolean function.

### How do I convert NOR gates to an AND gate?

To convert NOR gates to an AND gate, we'd do the following:

1. Feed input A to both input terminals of the first NOR gate. We'd get the output as the complement of A.

2. Repeat the process for input B with a second NOR gate to get the output as the complement of B.

3. Finally, pass these two outputs as the inputs to a third NOR gate. The NOR bit logic calculator will give the output as AB.

4. Thus, we see that we can use a combination of 3 NOR binary gates to get the AND output for the inputs A and B.

### What is NOR gate equal to?

A NOR gate is equivalent to an inverted-input AND gate. The NOR gate is one of the logical bitwise operators which produces an output of 1 if both the input bits are 0, and at all other times produces an output of 0.

### What is the difference between a NOR gate and an OR gate?

The NOR gate is a combination of an OR gate followed by an inverter. In other words, it inverts the output of an OR gate. So the NOR gate produces a true output only when both inputs are false, while it's the other way round for an OR gate.

### What is the difference between NAND and NOR?

A NAND gate inverts the output of an AND gate, while a NOR gate inverts the output of an OR gate. So in effect, a NAND gate gives a false output only when both inputs are true and a true output otherwise, while a NOR gate gives a true output only when both inputs are false, and a false output otherwise.

Binary representation
8-bit
Data type
Decimal
You can enter decimal numbers between -128 and 127.
First number
Second number
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