4 / 63 · 概念

NAND, NOR and inversion symbols

Track the scope of inversion and connect equivalent symbols with De Morgan’s laws.

尚無譯文，以下顯示課程原文。 (English)

The output circle complements the whole result

NAND complements AND; NOR complements OR:

Y_{NAND}=\overline{ab},\qquad Y_{NOR}=\overline{a+b}

For input order 00, 01, 10, 11, NAND gives 1, 1, 1, 0 and NOR gives 1, 0, 0, 0. An inverted output is still a valid logic signal.

An inversion circle changes the truth table

NAND · Truth table
a	b	y
0	0	1
0	1	1
1	0	1
1	1	0

Move inversions with De Morgan’s laws

\overline{ab}=\overline a+\overline b,\qquad \overline{a+b}=\overline a\,\overline b

Moving an output inversion^{inversion The NOT operation exchanges 0 and 1. An overline applies NOT to the entire expression covered by the line.} to both inputs also changes AND to OR, or OR to AND. Merely moving the circles preserves neither the symbol nor the function. At inputs 01, NAND gives 1 but an AND of the complemented inputs gives 0.

Move the output inversion

NAND: Y = NOT (a AND b)
Invert each input: Produce NOT a and NOT b
Combine with OR: Y = (NOT a) OR (NOT b)

Active-low describes assertion

An active-low^{active-low A convention in which a signal is asserted at 0. The suffix _n often marks this convention; the specification defines the behavior.} request is asserted at zero. The suffix _n is a naming convention, not an automatic circuit operation. If either of two active-low requests must trigger an active-high alarm, then

\mathrm{alarm}=\overline{\mathrm{req0\_n}}+\overline{\mathrm{req1\_n}}=\overline{\mathrm{req0\_n}\,\mathrm{req1\_n}}

Each short overline complements one named signal. The final long overline complements their AND as a whole, so a NAND implements this function. Inputs 11 mean no request and produce alarm=0; inputs 01 assert the first request and produce alarm=1. Keep a signal’s numeric value, asserted meaning and inversion symbols distinct.

自己試試看

Which gate gives go=1 only when both active-low permits permit0_n and permit1_n are asserted: NAND or NOR?

查看解說

NOR. Both permits are asserted at 00, so go=NOT(permit0_n OR permit1_n). The phrase “both asserted” must be interpreted using the signal polarity.