Free · Digital logic

Seven Boolean Gate Truth Results

Evaluate AND, OR, NOT, NAND, NOR, XOR and XNOR with binary inputs and accessible gate explanations.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

AND with A = 1 and B = 1 outputs 1.

Gate output is zero or one according to its complete truth table.

Worked example

Enter these known values and leave the other values blank.

GATE
AND
A
1
B
1
Gate value
1

Assumptions and limitations

  • Both inputs are binary selections. NOT uses only input A; the interface hides B in that mode.
  • The output is a logical truth value. This mathematical model does not simulate voltage thresholds or electronic timing.

Common questions

What distinguishes XOR from OR?

XOR outputs one when exactly one input is one; OR also outputs one when both are one.

What are NAND, NOR and XNOR?

They invert the outputs of AND, OR and XOR respectively.

References

Translate the complete captured seven-gate truth helper into local declarative Boolean arithmetic, preserving binary choices, conditional NOT input visibility and forward-only output. Suppress an output when a required binary input is cleared; NOT still requires only A. Replace external Boolean gate symbols with original accessible descriptions of every gate truth rule and input convention.

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