Binary to decimal: turning bits back into meaning
What this conversion does
It reads a string of 0s and 1s as a base 2 number and restates it in base 10. This is the direction you need when the value on screen is already in a machine format — a register dump, a mask, a flag byte — and the question you are asking is a human one, such as whether the value has crossed a threshold.
The weighted-sum method
Each binary digit stands for a power of 2 according to its position from the right, starting at 1, 2, 4, 8 and continuing. Sum the weights of the positions that hold a 1. For 10011100 those positions are 128, 16, 8 and 4, so the decimal value is 156. Once the first few weights are memorised — 1, 2, 4, 8, 16, 32, 64, 128 — the arithmetic is short addition.
Binary to decimal conversion table
Common bit patterns with their decimal values. The all-ones rows are the ones to remember: each is one less than the next power of 2, which is why 255 and 65535 turn up everywhere in computing.
| Binary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 1010 | 10 |
| 1111 | 15 |
| 10000 | 16 |
| 101010 | 42 |
| 11111111 | 255 |
| 100000000 | 256 |
Reading a flag or status byte
A status byte is not really a number, it is eight separate yes-or-no answers packed into one value. Converting it to decimal gives you a compact handle you can compare and log; the individual bits tell you what happened. Both readings are useful, and the conversion is what lets you move between a datasheet that documents bits and a log file that records decimals.
Watch the leading zeros
Leading zeros do not change the value — 0011 and 11 are both three — but they do change the width, and width is what tells you whether a field is one byte or four. When a value is copied out of a fixed-width field, keep the padding in your notes even though the converter ignores it.
Frequently asked questions
How do I read binary in my head?
Write the place values 128, 64, 32, 16, 8, 4, 2, 1 above the digits from the left for an eight-bit number, then add up the values above every 1. For 10011100 that is 128 + 16 + 8 + 4 = 156. Practising with eight bits covers the great majority of everyday cases.
Why does 11111111 equal 255 and not 256?
Because eight bits can represent 256 different values counting from zero, so the largest is 255. In general n bits reach 2 to the power of n minus 1. That off-by-one is the reason a byte holds 256 values but a value of 256 does not fit in one.
Can I paste binary with spaces between the bytes?
Yes. Spaces, tabs and underscores are ignored, so a string copied from a terminal or a memory dump converts without being cleaned up first. Grouping bits in fours or eights is a reading aid and carries no meaning of its own.
Does a leading 1 mean the number is negative?
Only if you have decided in advance that the field is signed two's complement, and that is a property of the format rather than of the bits. Taken on its own, 11111111 is simply 255. The converter treats every input as a non-negative magnitude unless you type an explicit minus sign.
What is the longest binary string I can convert?
Long enough for any value you are likely to paste — the tool works in exact integer arithmetic rather than floating point, so it does not degrade with size the way a calculator does. Extremely long inputs are rejected with a clear message rather than being silently truncated.