Two methods, 15 practice problems, and the shortcuts that make conversion second nature
Write the binary number. Below each bit, write its power-of-2 value, starting from 1 on the right and doubling each step left: 1, 2, 4, 8, 16, 32, 64, 128. Multiply each bit by its position value. Add all results. Example: 101101 — positions from right: 1,2,4,8,16,32. Bits with 1s: 32+8+4+1 = 45. Bits with 0s contribute nothing. For 8-bit binary, the position values are 128, 64, 32, 16, 8, 4, 2, 1. This is the most intuitive method and the one taught in computer science courses.
Start with result = 0. Process bits left to right. For each bit: double the current result, then add the bit value. Example: 101101. Start 0, double=0, add 1→1. Double→2, add 0→2. Double→4, add 1→5. Double→10, add 1→11. Double→22, add 0→22. Double→44, add 1→45. This method never needs to know position values and works for binary numbers of any length. Programmers prefer this method because it translates directly to a simple loop.
1) 0001 = ? (Answer: 1)
2) 0010 = ? (Answer: 2)
3) 0101 = ? (Answer: 5)
4) 1010 = ? (Answer: 10)
5) 1111 = ? (Answer: 15)
6) 00101010 = ? (Answer: 42)
7) 01111111 = ? (Answer: 127)
8) 10000000 = ? (Answer: 128)
9) 11001001 = ? (Answer: 201)
10) 11111111 = ? (Answer: 255)
11) 00011001 = ? (Answer: 25)
12) 01100110 = ? (Answer: 102)
13) 10101010 = ? (Answer: 170)
14) 01010101 = ? (Answer: 85)
15) 00110110 = ? (Answer: 54)
Check your answers with our binary to decimal calculator. For bulk conversions, use the binary to text converter which processes entire strings at once.