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.
       

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Multiplication of two octal numbers.

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

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

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

Since Octal Numbers are from 1 to 8 so there are following steps in this procedure:

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

Step 2)   Now the result is divided by 8.

Step 3)   If we get any remainder in step 2 we put it as result otherwise we put 0 as result.

Step 4)   The quotient of step 2 becomes the carry for its left digits.

For example
                  Suppose two numbers are 6₈ × 23₈ 

Step 1)    6*3=18

Step 2)   18/8=>  quotient=2 and remainder=2

Step 3)  result=2   (remainder)

Step 4) carry=2   (Quotient)

now again,    for  6*2

Step 1)  6*2=12  
              12+2 =14   (where 2 is carry)

Step 2)  12/8=>   quotient=1 and remainder=4

Step 3)  result=4   (remainder)

Step 4) carry=1   (Quotient)


Since the multiplication is complete thus the result is 162_8.
         

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