MULTIPLY

  

DECIMAL

A multiplication problem is written with one number on top, called the multiplicand, and one number on the bottom, called the multiplier.

The multiplication phase, the digits of the multiplier are stepped through one at a time, from right to left.

For example, let’s multiply 3.87 and 5.3:

  In simple words, this operation does not have different with our math modern.

BINARY

Binary is actually much simpler than decimal multiplication. In binary multiplication, we only need to remember the following,

0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1


example:


101 times 11;

First we multiply 101 by 1, Then we put a 0 as a placeholder as we would in decimal multiplication, and multiply 101 by 1


101
x11
101
1010 <-- the 0 here is the placeholder

The next step is to add. We must add 101 and 1010, the answer is 1111.

    101
  x  11

ーーー

     101 

+ 1010

一一一
    1111

HEXADECIMAL

While multiplying, if the product consists of two digits, the digit on the left is carried over and added to the product in the next place.

Example:

Find the product of 1A8₁₆ and AF23

                             

              6 5 ← Digits carried over in second multiplication
              9 7 ← Digits carried over in first multiplication.
          1 A 8
          x A F
    ---------------
        1 8 D 8
      1 0 9 0 0
  ----------------------
     1 2 1 D 8
 -----------------------


First the digit F in the number AF16 is multiplied with each of the digits in the number 1A816.

F x 8 = 78.

The digit 8 is written below in the product row and 7 is carried over to the next place to be added with the next product.

F x A = 9616

and 9616 + 716 = 9D16.

D is written in the product row and 9 is carried over to the next place

F x 1 = F.

and F16 + 916 = 1816 .

The second row of multiplication is done in a similar manner, by multiplying the digit A with each of the digits in 1A816.

The two products are then added to get the final product.

Thus 1A816 x AF16 = 121D816.