Decimal to Binary

Binary is a place-value system with only two digits, 0 and 1, so every decimal number must be rewritten as a sum of powers of 2. Repeated division by 2 works because each division step separates the number into a quotient and a remainder: the remainder tells you whether the current power of 2 is needed (1) or not (0). Reading the remainders from bottom to top gives the binary digits in the correct order.

Use this when converting a whole number from base 10 into binary for computer science, digital electronics, or low-level programming. It is also useful when understanding how memory addresses, bit patterns, and machine data are represented.

• Reading the remainders from top to bottom instead of bottom to top
• Forgetting to stop when the quotient reaches 0
• Mixing up the quotient and remainder at each division step