Computing · Foundations
Binary–decimal conversions
The method first, the answer second. Try it on paper and check every step.
From decimal to binary
Divide the number by 2 and write down the remainder. Repeat with the quotient until you reach 0. Read the remainders from bottom to top.
45 → 22 remainder 1 → 11 remainder 0 → 5 remainder 1 → 2 remainder 1 → 1 remainder 0 → 0 remainder 1. Result: 101101₂.
From binary to decimal
From the right, the place values are 1, 2, 4, 8, 16, 32… Add the values where the digit is 1: 101101₂ = 32 + 8 + 4 + 1 = 45₁₀.
Now try it yourself
Convert 13 and 26 to binary; convert 1010 and 11001 to decimal.
Check the answers
13 = 1101₂; 26 = 11010₂; 1010₂ = 10; 11001₂ = 25.