The XOR Gate: Truth Table and Symbol

The XOR gate (exclusive OR) takes two inputs and produces an output of 1 only when the inputs are different. XOR is a crucial gate in computer science, used extensively in encryption and arithmetic circuits. This is covered in OCR J277 Section 2.5.

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How the XOR Gate Works

XOR stands for exclusive OR. Unlike the standard OR gate (which outputs 1 when at least one input is 1), XOR outputs 1 only when exactly one input is 1 — that is, when the inputs are different from each other.

In Boolean algebra, XOR is written as:

• A XOR B
• A ⊕ B (a circled plus symbol)

The word "exclusive" means it excludes the case where both inputs are 1.

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XOR Gate Truth Table

A	B	A XOR B
0	0	0
0	1	1
1	0	1
1	1	0

Compare this with the OR truth table — the only difference is the last row. When both inputs are 1, OR outputs 1 but XOR outputs 0.

A	B	OR	XOR
0	0	0	0
0	1	1	1
1	0	1	1
1	1	1	0

OCR Exam Tip: The key difference between OR and XOR is the last row. OR gives 1 when both inputs are 1; XOR gives 0. Think of XOR as "one or the other, but not both."

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XOR Gate Circuit Symbol

The XOR gate symbol looks like the OR gate but with an extra curved line on the input side:

  A ----\\       /---- Q
        ||  XOR |
  B ----//       \

The double curved line on the left distinguishes XOR from OR. In the exam, you must draw this extra line to get the mark.

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XOR in Programming

Python does not have a dedicated xor keyword for Boolean values, but you can use the != operator or the bitwise ^ operator:

# XOR using != (not equal)
a = True
b = False
result = a != b  # True (because they are different)
print(result)

# XOR using bitwise ^ operator
x = 1
y = 0
print(x ^ y)  # 1

In OCR pseudocode, XOR may be expressed as:

a = true
b = false
if a != b then
    print("Inputs are different")
endif