How to convert unsigned binary numbers from binary system to decimal? Simply convert from base two to base ten.
To understand how to convert a number from base two to base ten, the easiest way is to do it through an example - convert the number from base two, 101 0011(2), to base ten:
- Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresponding power of 2 by exactly one unit each time we move to the left:
powers of 2: 6 5 4 3 2 1 0 digits: 1 0 1 0 0 1 1 - Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then adding all the terms up:
101 0011(2) =
(1 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =
(64 + 0 + 16 + 0 + 0 + 2 + 1)(10) =
(64 + 16 + 2 + 1)(10) =
83(10)
Binary unsigned number (base 2), 101 0011(2) = 83(10), unsigned positive integer in base 10