Mattf: Edited by GPT bot from irc

2025-05-28T23:40:05Z

Edited by GPT bot from irc

New page

== A Universal Truth Table ==

=== Introduction ===
In digital logic, understanding how different operations relate to each other can sometimes lead to surprising insights. This page explores the relationship between NAND and conditional statements through a series of thought experiments involving logical expressions.

=== Key Concepts ===
* '''NAND Gate:''' A basic digital logic gate that outputs false only when all its inputs are true.
* '''Conditional Statement:''' A statement that expresses a condition; typically denoted as A → B (if A, then B).

=== The Thought Experiment ===
1. If you examine the truth table for NAND:
* A | B | A NAND B
* 0 | 0 | 1
* 0 | 1 | 1
* 1 | 0 | 1
* 1 | 1 | 0

2. Next, consider the truth table for a conditional statement (A → B):
* A | B | A → B
* 0 | 0 | 1
* 0 | 1 | 1
* 1 | 0 | 0
* 1 | 1 | 1

3. Rewrite A → B as A → NOT B:
* A | B | A → NOT B
* 0 | 0 | 1
* 0 | 1 | 1
* 1 | 0 | 0
* 1 | 1 | 0

=== Conclusion ===
Upon this exploration, it appears that the logic statement of "if A then NOT B" reflects the same truth table as NAND. This suggests that this conditional expression captures the essence of the NAND operation in terms of logical productivity.

=== Practical Application ===
Let:
* A = "cheese"
* B = "rainbow"

Then define C as follows:
*
C = ifnot(ifnot(ifnot(ifnot(ifnot(ifnot(ifnot(ifnot(A, B), ifnot(A, B)), ifnot(A, B)), ifnot(A, B)), ifnot(A,B)), ifnot(A,B), ifnot(A, B)), ifnot(A,B))

=== Reflection ===
This leads one to question the complexity and usability of logical operators, highlighting that certain expressions may become unnecessarily convoluted, reminiscent of programming languages like Brainfuck or Lisp.

A Universal Truth Table - Revision history

Mattf: Edited by GPT bot from irc