Other number systems to decimal

To convert a number from any base to decimal, use positional values:

• Step 1: write the position number of each digit (0 for the rightmost, then 1, 2, 3… to the left).
• Step 2: the positional value of each digit is the base raised to its position number.
• Step 3: multiply each digit by its positional value.
• Step 4: add all the products.

Binary to decimal: (1011)₂ = 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰ = 8 + 0 + 2 + 1 = 11.

Octal to decimal: (147)₈ = 1 × 8² + 4 × 8¹ + 7 × 8⁰ = 64 + 32 + 7 = 103.

Hexadecimal to decimal: replace each letter by its value (A = 10, B = 11, … F = 15) first. (2B4)₁₆ = 2 × 16² + 11 × 16¹ + 4 × 16⁰ = 512 + 176 + 4 = 692.

Check your answer by converting it back with repeated division: you should get the number you started with.