Now that the fundamentals of addition and subtraction are under our belt, multiplication and division will be a cinch.

The great part about binary multiplication is that you only need to know your multiplication table up to 1!

Yep, it’s really that easy!

Here is the long-form standard decimal multiplication problem, 120 x 15:

   120
  x 15
  ----
   600  
+ 1200 
  ----
  1800 <- Final answer

Binary multiplication follows this exact same process, multiply and then add the results together. For larger multiplication problems you would repeat step 3 as many times as the bottom number is long.

Let’s do the same problem, 120 x 15 except in binary.

1. Line up problem, larger number on top, place values aligned:

     1111000
    x   1111
    --------

2. Multiply the top number by 1 of the LSB of the bottom number:

     1111000
    x   1111
    -------^
     1111000

3. Add a 0 to the next row and multiply all the top numbers by the next LSB (repeat as necessary):

     1111000
    x   1111
    ------^-
     1111000
    11110000

4. Repeat the same process for the next bit

     1111000
    x   1111
    -----^--
     1111000
    11110000
   111100000

5. Repeat the same process for the next bit

      1111000
     x   1111
     ----^---
      1111000
     11110000
    111100000
   1111000000

6. Add the results together

       1111000 
      x   1111 
      -------- 
       1111000 <- Add
      11110000 <- all
     111100000 <- these
    1111000000 <- together
    ----------
   11100001000 <- Final Answer