Bitwise NOR: 0011 0110 ↓ 0100 0001 — NOR gate

exam standardOR then complement

Answer

10001000

Why this example is worth doing

Like NAND, no mainstream instruction set exposes NOR directly, so the byte-wide result is computed as an OR followed by a NOT. The page notes the historical exception — some architectures shipped NOR precisely because it was the cheap primitive — and uses it to observe that instruction sets are shaped by what was cheap when they were designed, which is why they disagree about which logical operations deserve an opcode.

Try your own input in the NOR gate. Truth table, symbol and algebraic form for (A + B)′, the other universal gate.

How the answer is reached

Column by column

A00110110

B01000001

result10001000

Column by column — columns bit, A, B, result
bitABresult
7001
6010
5100
4100
3001
2100
1100
0010

Compare with

Open the NOR 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