Number bases: watch it solved step by step

Convert between decimal and binary, octal, hexadecimal or any base: repeated division for the whole part, repeated multiplication for the fraction. Level: KS3 / A-level. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: convert 255 to binary

The question. We write the decimal number 255 in binary (base 2). In base 2, each place is worth 2 times the place to its right, and only the digits 0, 1 are used. The whole part and the fractional part are converted in different ways.
Whole part: divide by 2 again and again. To convert the whole part 255, divide by 2, write down the remainder, then divide the quotient by 2 again. Stop when the quotient reaches 0. The remainders, read from the bottom up, are the digits.
255 ÷ 2 = 127 remainder 1. 255 ÷ 2 = 127 with remainder 1. Carry on with the quotient 127.
127 ÷ 2 = 63 remainder 1. 127 ÷ 2 = 63 with remainder 1. Carry on with the quotient 63.
63 ÷ 2 = 31 remainder 1. 63 ÷ 2 = 31 with remainder 1. Carry on with the quotient 31.
31 ÷ 2 = 15 remainder 1. 31 ÷ 2 = 15 with remainder 1. Carry on with the quotient 15.
15 ÷ 2 = 7 remainder 1. 15 ÷ 2 = 7 with remainder 1. Carry on with the quotient 7.
7 ÷ 2 = 3 remainder 1. 7 ÷ 2 = 3 with remainder 1. Carry on with the quotient 3.
3 ÷ 2 = 1 remainder 1. 3 ÷ 2 = 1 with remainder 1. Carry on with the quotient 1.
1 ÷ 2 = 0 remainder 1. 1 ÷ 2 = 0 with remainder 1. The quotient is 0, so we stop.
Read the remainders from the bottom up. The last remainder is the leftmost digit. Reading upwards gives 11111111.
Put the two parts together. Whole part 11111111, then the point, then the fractional digits (none: it is a whole number). So 255 in base 2 is 11111111.

Answer: 11111111 in base 2

Practise number bases with problems the Lab marks for you.