What if you only had two fingers?
You’d count the same way — but run out of symbols faster. Instead of carrying at ten, you carry at two. That’s the entire difference between decimal and binary.
Two digits only: 0 and 1. No 2, no 3 — the moment you reach two,
you carry left.
So you count: 0, 1 — then carry: 10, 11 — carry again: 100, 101,
110, 111 — carry again: 1000 …
Binary = base-2 — two symbols, positional value, carry at two.
The position still means everything, but now each step left multiplies by two, not ten:
In 1011:
1→1 × 1=11→1 × 2=20→0 × 4=01→1 × 8=8
Total: 11 in decimal.
Why does a machine speak this language? Because 0 and 1 map perfectly
to off and on — the only two states a transistor knows. Binary isn’t
arbitrary. It’s the simplest possible counting system, and simplicity is
what electronics can sustain at billions of operations per second.
The Pattern
2⁰ → 2¹ → 2² → 2³ → ...
1 → 2 → 4 → 8 → 16 → 32 → 64 → 128 → ...
Decimal carries at ten. Binary carries at two. Same logic — different base.