SR latch from two cross-coupled NANDs — NAND gate

exam standardthe memory element

Answer

Q⁺ = 1

Why this example is worth doing

Two NANDs, each feeding the other, form an active-low SR latch — the first sequential circuit most students build. Inputs idle at 1 and are asserted by pulling low, which is why the labels carry overbars, and driving both low at once produces the forbidden state where both outputs go high and the next value depends on which input releases first. The page names it a race rather than calling it undefined, and hands off to the flip-flops page.

Try your own input in the NAND gate. Truth table, symbol and algebraic form for (A·B)′, the universal gate.

How the answer is reached

The probed row

Sn = 1, Rn = 1, Q = 1

Output table

Output table — columns Sn, Rn, Q, Q⁺
SnRnQQ⁺
0001
0011
0101
0111
1000
1010
1100
1111

Compare with

Open the NAND gate

This input is entered in the tool itself — it is too rich for a link to carry.

Note:

Notation this page assumes

  • Symbols: · is AND, + is OR, ⊕ is XOR, a prime or an overline is NOT. The field also takes ∧ ∨ ¬ ~ ! & | and the words.
  • Operator precedence, tightest first: NOT, then AND (including juxtaposition), then XOR/XNOR, then NAND/NOR, then OR, then IMPLIES, then IFF.
  • Gate symbols follow whichever standard the header toggle is set to: ANSI/IEEE Std 91-1984 distinctive shapes, or IEC 60617-12 rectangles.

Sources

  • ANSI/IEEE Std 91-1984, Graphic Symbols for Logic Functions
  • IEC 60617-12, Graphical Symbols for Diagrams — Binary Logic Elements
  • Sheffer, “A Set of Five Independent Postulates for Boolean Algebras” (1913)