Mastering Reverse Engineering

Binary arithmetic

Since a byte is the common unit used in computers, let's play with it. We can start with basic arithmetical functions: addition, subtraction, multiplication, and division. The pencil-and-paper method is still a strong method for doing binary math. Binary arithmetic is similar to doing arithmetic in decimal numbers. The difference is that there are only two numbers used, 1 and 0.

Addition is carried out as follows:

  1b               10101b+ 1b             +  1111b  10b              100100b

An example of subtraction is as follows:

 10b               1101b- 1b              - 111b   1b                110b

Multiplication is carried out as follows:

   101b             1b x 1b = 1bx   10b             1b x 0b = 0b   000  101     1010b

Division in binary works as follows:

       1010b                         1000b 10b | 10100b                  11b | 11010b     -10                           -11        010                           0010       -10                           -000 ...