Bitwise NAND: 1011 0110 ↑ 0110 1101 — NAND gate

exam standardno processor has this instruction

Answer

11011011

Why this example is worth doing

Computing a bitwise NAND requires an AND followed by a NOT, because essentially no instruction set offers NAND directly — even though it is the cheapest gate in silicon. The page uses that gap to make a point about levels of abstraction: what is primitive at the transistor level is composite at the instruction level, and neither ordering is wrong. The worked bytes make the two-step nature concrete.

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

Column by column

A10110110

B01101101

result11011011

Column by column — columns bit, A, B, result
bitABresult
7101
6011
5110
4101
3011
2110
1101
0011

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)