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 = 1b
x   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
         00                            10b (remainder)
         -0
          0