Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2013-01-21 08:03:47

reallylongnickname
Full Member

Offline

### boolean rule

Last edited by reallylongnickname (2013-01-21 10:12:58)

## #2 2013-01-26 14:09:02

John E. Franklin
Star Member

Offline

### Re: boolean rule

1 = 1 | 0
0 = 0 | 0
| means OR.
now AND...
0 = 0 & X
X = 1 & X, where X can be 1 or 0 (boolean value)
now XOR...
(exclusive-OR)
1 = 1 ^ 0
1 = 0 ^ 1
0 = 1 ^ 1
0 = 0 ^ 0
basically the 1 is a toggle of the other value, toggle = flip from 0 to 1 or 1 to 0.
Given that Ab, Bb, Cb are boolean variables holding 0 or 1, we have the following:
The / sign is the negation or NOT symbol as / put in front of a variable.

(Ab & /Bb) | (Bb & /Ab) = A ^ B, where ^ means exclusive-or (XOR).

Also demorgans laws something like...
/(Ab & Bb) = /Ab + /Bb

Also see Karnaugh mapping for electronics ways...

Maurice Karnaugh of Bell Labs 1957 1953...

Imagine for a moment that even an earthworm may possess a love of self and a love of others.