Binary to decimal converter

Type a binary number, made of 0s and 1s, and its decimal value appears as you type. Several numbers can go in at once, separated by spaces, commas or new lines. A prefix is fine when it matches the base, like 0x on hex or 0b on binary. So is the _ character used to group digits, as in 1001_1100. Numbers can be as long as you like and can be negative, but they have to be whole: there's no decimal point.

This converts numbers. To turn binary back into letters and words, use the binary translator instead.

Show the steps opens the working under the answer, line by line, the same way you'd set it out on paper. It shows the first four numbers when there are several.

Write the place values over the bits, starting from 1 on the right and doubling each time: 1, 2, 4, 8, 16, 32, 64, 128. Add up the place values that have a 1 under them and skip the ones with a 0.

For 10011100 the 1s sit under 128, 16, 8 and 4. 128 + 16 + 8 + 4 is 156.

Unix file permissions are three bits each, one bit for read, one for write and one for execute, which is why they're written in octal. Read is worth 4, write 2 and execute 1, and each octal digit adds up one set, for the file's owner, its group and everyone else in turn. A mode of 754 gives the owner 4 + 2 + 1, everything, the group 4 + 1, read and execute, and everyone else 4, read only.

To check a conversion, go back the other way by halving. 156 halves to 78 with nothing left over, 78 to 39 with nothing, 39 to 19 remainder 1, 19 to 9 remainder 1, 9 to 4 remainder 1, 4 to 2 with nothing, 2 to 1 with nothing, and 1 to 0 remainder 1. Read the remainders from the last one up: 10011100, the number you started with. The decimal to binary converter sets this out step by step.

Ages 8 and up, about 20 minutes. Five pupils stand in a row holding cards worth 16, 8, 4, 2 and 1. Each card is either shown (1) or hidden (0). Call out a number and the row works out which cards to show; then show a pattern and the class reads the number.

Take it further: with five cards the biggest number is 31. Ask what a sixth card would be worth and how far it lets them count. CS Unplugged's binary numbers lessons build on the same cards.