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Logic reference

Digital logic truth tables reference

Explore NOT, AND, OR, NAND, NOR and XOR using 1 and 0. Print individual digital truth tables, a combined comparison and common Boolean notation aliases.

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Use 1 for true and 0 for false. Compare the digital output with the named operation.

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The notation changes; the truth conditions do not

Digital logic uses 1 and 0 for true and false. The reference also explains common aliases such as a prime for NOT, a dot for AND and a plus sign for OR.

These pages teach Boolean operations. The plus sign in this context is not an instruction to perform ordinary integer addition.

Learning objective

What this activity builds

Connect Boolean operators with binary truth values while distinguishing logic notation from ordinary arithmetic.

Worked example

What is the NAND output when both inputs are 1?

0.

AND returns 1 for two true inputs. NAND negates that result, so it returns 0.

Teaching notes

Make the practice count

  • Start with AND and NOT before combining them as NAND.
  • Compare OR with NOR in the same way.
  • Explain that p + q can mean Boolean OR in digital notation.
  • Use XOR to identify rows where the two inputs differ.

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Math SheetNameScoreTeacherDateDigital Logic Truth TablesRead digital truth tables with 1 for true and 0 for false.1 = T; 0 = FNOTNOT is true exactly when its input is false. Given: NOT p / p'.(p)p(p)1001ANDAND is true only when both inputs are true. Given: pq / p·q.(pq)pq(pq)111100010000OROR is true when at least one input is true. Given: p+q.(pq)pq(pq)111101011000math-sheet.comPage 1 / 3
Math SheetNameScoreTeacherDateDigital Logic Truth TablesRead digital truth tables with 1 for true and 0 for false.1 = T; 0 = FNANDNAND is the negation of AND, so it is false only when both inputs are true.(pq)pq(pq)110101011001NORNOR is the negation of OR, so it is true only when both inputs are false.(pq)pq(pq)110100010001XORXOR is true when exactly one input is true.(pq)pq(pq)110101011000math-sheet.comPage 2 / 3
Math SheetNameScoreTeacherDateDigital Logic Truth TablesRead digital truth tables with 1 for true and 0 for false.1 = T; 0 = FTruth table1 = T, 0 = Fpq(p)(pq)(pq)(pq)(pq)(pq)11011000100011010110110100100110math-sheet.comPage 3 / 3

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