How to Convert Binary Numbers to Decimal (and Back)

At its heart, counting is just a way of grouping numbers. In our everyday decimal system, we use ten digits and group by powers of ten: ones, tens, and hundreds. Computers, however, rely on binary, a base-two system using only zeros and ones, mirroring hardware switches that are either off or on. Translating between these systems is simple once you understand placeholders.

To convert binary to decimal, read the binary digits from right to left, assigning each position a power of two, starting with one, then doubling each time. If a digit is one, you count that value; if it is zero, you ignore it. For example, the binary number 1011 translates to one eight, zero fours, one two, and one one. Adding these together—eight plus zero plus two plus one—gives us eleven in decimal.

Going from decimal to binary is the reverse. One intuitive method is to subtract the largest possible power of two from your number and repeat the process. Let us convert thirteen. The largest power of two that fits in thirteen is eight, leaving five. The largest power of two in five is four, leaving one. Two does not fit into one, but one does. Writing a one for the positions we used (eight, four, and one) and a zero for the one we skipped (two) yields 1101. This simple arithmetic bridges the gap between human thought and digital logic.