Two live instruments. The first turns text into raw ASCII bytes you can toggle bit by bit. The second shows De Morgan’s laws holding true — as switches, as truth tables, and as eight parallel bits at once.
Type anything. Each character becomes one byte, most significant bit first. Click any bit to flip it — the character, the decimal value and the hex all follow.
A = 0100 0001,
a = 0110 0001. One flip, whole other
letter.
Negation turns AND into OR and OR into AND. Toggle the two inputs and both sides of each identity stay locked together — that is the whole law, visible at a glance.
Shade first and invert, or invert first and combine — both routes land on the identical region. The dot marks where your current A and B switches sit, so a filled dot means that expression is true right now.
The highlighted row is your current switch position. The two boxed columns in each pair never disagree.
| A | B | A ∧ B | ¬(A ∧ B) | ¬A ∨ ¬B | A ∨ B | ¬(A ∨ B) | ¬A ∧ ¬B |
|---|
The same law, applied bitwise to two bytes. Toggle the bits of A and
B: ~(A&B) and
~A|~B come out identical every time —
which is exactly why compilers and hardware trade one for the other
freely.