Deep down, a computer is a vast collection of switches, each either off or on. There is no "maybe" and no "a bit on". With only these two states, every photo, song, message and game must be built from just two symbols: 0 and 1. This is binary, and once you can read it, you can see how the machine really thinks.
Denary — the counting you already know
The everyday numbers you use are denary (base 10), because each column is worth ten times the one to its right: units, tens, hundreds, thousands. We use ten digits (0–9) because humans have ten fingers. A computer has, in effect, two fingers — off and on — so it counts in base 2.
Binary place values
In binary each column is worth twice the one to its right. Reading from the right they are 1, 2, 4, 8, 16, 32, 64, 128. Eight of these columns make one byte. Each single 0 or 1 is called a bit (short for binary digit). Think of it like packing a suitcase using only fixed-size blocks — 128, 64, 32 and so on — and you may use each block once.
| Place value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|---|
| Bit | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |
Denary to binary
Work left to right along the headings. Ask of each: "Does it fit into what's left?" If yes, write 1 and subtract it; if no, write 0 and move on.
Start with 100. 128? Too big → 0. 64? Fits, 100 − 64 = 36 → 1. 32? Fits, 36 − 32 = 4 → 1. 16? No → 0. 8? No → 0. 4? Fits, 4 − 4 = 0 → 1. 2? No → 0. 1? No → 0.
Reading the bits: 0110 0100. Check: 64 + 32 + 4 = 100. ✓
Binary to denary
The reverse is easier: write the headings above the bits, then add up the values sitting above every 1. For 0100 1101 that is 64 + 8 + 4 + 1 = 77.
Tip: memorise the eight place values 128 64 32 16 8 4 2 1 like a times-table. Once they are automatic, every conversion in this whole strand becomes fast and reliable.