The binary number system uses only two digits (0 and 1) to represent all numbers, using powers of 2 as place values. Each digit position corresponds to 2^n for some n ≥ 0, so the binary number 1011 equals 1×8 + 0×4 + 1×2 + 1×1 = 11 in decimal. Computers use binary because electronic circuits naturally represent two states: on (1) and off (0). Converting between binary and decimal is a core skill for understanding how data is stored and processed.
Practice converting between binary and decimal in both directions. Start with small numbers (0–15) to build intuition about powers of 2, then extend to larger values. Use the doubling/halving method for quick conversions.
If you have studied place value in decimal, you already understand the core idea of binary — the systems work identically, just with a different base. In decimal (base 10), each position is worth ten times the one to its right: the number 253 means 2×100 + 5×10 + 3×1. Binary (base 2) works the same way, but each position is worth *two* times the one to its right: the positions represent 1, 2, 4, 8, 16, 32, and so on — successive powers of 2.
To convert binary to decimal, multiply each bit by its place value and sum the results. The binary number 1011 means 1×8 + 0×4 + 1×2 + 1×1 = 11. To convert decimal to binary, repeatedly divide by 2 and record the remainders from bottom to top: 11 ÷ 2 = 5 R1, 5 ÷ 2 = 2 R1, 2 ÷ 2 = 1 R0, 1 ÷ 2 = 0 R1 — reading remainders upward gives 1011. Both directions are worth practicing until they feel mechanical.
Computers use binary because of physics, not convention. A transistor — the fundamental building block of all modern processors — is a switch that is either open or closed, conducting or not. That's two states, which map naturally to 0 and 1. Every piece of data your computer handles — integers, text, images, programs — is ultimately stored and processed as sequences of these bits. Understanding binary lets you reason about what's actually happening at the hardware level.
One thing that trips up beginners: binary numbers follow all the same arithmetic rules as decimal. You can add, subtract, multiply, and divide in binary just like in decimal — carrying and borrowing work the same way, just with 2 as the threshold instead of 10. For example, 1 + 1 in binary equals 10 (zero with a carry), exactly as 9 + 1 equals 10 in decimal. This isn't a new kind of math; it's the same math in a new base.