Converting Between Binary and Decimal

Every number system assigns a value to each position a digit sits in. In decimal, the places are 1, 10, 100, 1000 — powers of ten. In binary, the places are 1, 2, 4, 8, 16, 32, 64, 128 — powers of two. A binary digit, or bit, can only be 0 or 1, so each place either counts fully or not at all. That is why building a binary number feels like making change using only coins worth powers of two: you decide, place by place, whether that coin fits.

To convert decimal to binary, divide repeatedly by 2 and keep track of the remainders. Each division asks whether the current amount is odd or even — the remainder, 0 or 1, becomes one bit. Reading the remainders from last to first gives the binary number. To go the other direction, binary to decimal, multiply each bit by the place value of its position and add up the results. A 1 counts that place's full value; a 0 contributes nothing.

This skill is the foundation for everything else in the data unit. Before you can talk about mixing colors with RGB values or compressing an image, you need to trust that a string of bits is really just a number written in a different base, and that the number of bits available limits how large a value can be stored. Comparing binary numbers also depends on this: more digits does not automatically mean a bigger value, since leading zeros cost nothing.