Binary & decimal converter
MathNo. 02 / 24approved
Two directions, one widget: binary to decimal and decimal to binary, with the powers of two shown. Ones and zeros, dressed up and sent home.
there are 10 kinds of people — those who get this joke, and those who don't.
work surface
Math, not advice — results are indicative. Read the disclaimer.
most-used utilities
IP octet
11111111 is 255, the friendliest byte. Your router agrees.
ASCII "A"
01000001 is 65, which is "A". Hello, letters.
Bit twiddler
00001111 is 15. Four bits on, four bits off — perfectly balanced.
Nice number
69 in binary is 1000101. Nice, in any base.
Power of two
256 is 2^8. Eight bits, all for one.
Byte magic
10101010 is 170. The eighties called, they want their byte back.
pro tips
Every bit to the left doubles. It's powers of two wearing a trench coat.
If a number feels weird in decimal, it's probably elegant in binary. 255 is 11111111 — proof.
Count on your fingers: each finger is a bit. You can reach 1023 without running out of hands. Mostly.
what it does
Both directions in one place. Paste some binary and watch it become decimal; type a number and watch it go back to ones and zeros. Everything updates as you type, and it never asks for your permission.
Binary to decimal is just adding up the powers of two where the ones sit — we even show the math, because nobody trusts a number that appears out of nowhere. Decimal to binary works the other way: it figures out which powers of two fit, from biggest to smallest.
Handy for IP octets, ASCII codes, bit flags and impressing people at parties (nobody is impressed, we know, but the feeling of converting 255 in your head is a private joy).
It's also the quiet engine of everything digital: colours, characters and numbers all live as bits under the hood. Reading a few of them is like peeking behind the curtain of the machine — the curtain is ones and zeros, and it's never coming back.
quick answers
How do you read binary?
Each digit is a power of two, doubling left to right. Add the powers where the ones sit: 1011 is 8 + 2 + 1 = 11.
What is 255 in binary?
It's 11111111 — all eight bits on, the largest value a single byte can hold. The friendliest number in networking.
Why do IP octets cap at 255?
Because each octet is a byte of eight bits, and eight bits max out at 255. That's why 192.168.1.255 works and 192.168.1.256 doesn't.
Can it handle very large numbers?
Yes — up to 2^53, beyond which the exact integers run out in JavaScript. Past that, we gently say it's a lot of bits.