Single-literal term

Also called: single literal, single-literal factor, lone literal, single literal term

A term made of just one literal, such as C' in AB + C'. It needs no first-level gate, and in NAND-NAND or NOR-NOR it enters the output gate complemented.

A single-literal term is a product (or sum) with only one literal: C in , or in .

In an AND-OR circuit it needs no AND gate: the wire goes straight into the OR. That is why it costs only one gate input in the gate input count.

The NAND-NAND catch. The output NAND of a NAND-NAND circuit inverts each input before ORing them (by De Morgan, a NAND is an OR with bubbled inputs). A product term arrives already inverted from its first-level NAND, so that works out. A single literal has no first-level gate, so you must feed its complement:

For F = , the output NAND gets and . Then = .
Reading it back: a plain wire C into the output NAND means a term.

The same rule holds for NOR-NOR: a single-literal factor enters the output NOR complemented. See two level logic.

Worked example

Example

NAND-NAND with a single literal

Build F = in NAND-NAND form. The circuit above is the result (inverters shown for the complemented inputs).

1.
has two literals: first-level NAND(A, ) gives .
2.
C is a single literal: no first-level gate. Feed its complement, , into the output NAND.
3.
Output: NAND(, ) = .
4.
Check A = 0, B = 0, C = 1: g1 = NAND(0, 1) = 1, and = 0, so F = NAND(1, 0) = 1. The SOP gives 0 + 1 = 1. ✓

Common mistakes

Wiring the single literal straight into the output NAND uncomplemented, which implements instead.
Giving the single literal its own one-input NAND without realizing that is just an inverter. That also works, but costs a gate.

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Single-literal term is taught in Boolean Simplification.

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