Multiplication of two Hexadecimal Numbers

If we have given two Hexadecimal numbers then there are two ways by which we can get the multiplication of these numbers:

1) By direct multiplication of Hexadecimal Numbers
2) By first converting these Hexadecimal Numbers to Binary Numbers then multiply these numbers and then convert this result in Hexadecimal again.

 So here i will explain the first method since second method is simple and easy to use.

 There are following steps in this procedure:

Step 1)  First we will multiply numbers as decimal numbers and add carry if any.

Step 2)   If we get any remainder in step 2 we put it as result (in hexadecimal format) otherwise we put 0 as result.

Step 3)   The quotient of step 2 becomes the carry for its left digits.

For example
Find the product of 1A8₁₆ and AF₁₆.
                               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
                   ---------------------------

Step 1)    F x 8 = 78.

Step 3)  result=8

Step 4) carry=7

Similarly other digits are multiplied.

F x A = 96₁₆
and 96₁₆ + 7₁₆ = 9D₁₆.

F x 1 = F.
and F₁₆ + 9₁₆ = 18₁₆ .

Since the multiplication is complete thus the result is 1A8₁₆  x  AF₁₆ = 121D8₁₆.