How does the binary number system work?
Same way the decimal system or any other base number system works. Reading from right to left, you take that digit and multiply it by the base raised to the column number (with column numbers counting from 0, by 1s). Then you add the values up. example of why 714 = 714: you take the sum of: 4 x 10 ^ 0 1 x 10 ^ 1 7 x 10 ^ 2 which becomes 4 x 1 = 4 1 x 10 = 10 7 x 100 = 700 Add them up and you get 714 So, 1011001 in base 2 (binary) would be the sum of: 1 x 2 ^ 0 0 x 2 ^ 1 0 x 2 ^ 2 1 x 2 ^ 3 1 x 2 ^ 4 0 x 2 ^ 5 1 x 2 ^ 6 which becomes 1 x 1 = 1 0 x 2 = 0 0 x 4 = 0 1 x 8 = 8 1 x 16 = 16 0 x 32 = 32 1 x 64 = 64 Add them up, and 1011001 represents 89 in base 10.
