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Multiply 9910 times 9910 : 9801

How many decimal places does each operand (99) take: 2.

How many decimal places does the result take: 4.

Twice the Number of Places

        10110111            B7          183 
        10100010            A2          162 
        ————————            ——          ———
        00000000           16E          366
       10110111.          726.        1098
      00000000..                      183
————————————————          ————        —————
 111001111001110          73CE        29646 

The product of two N-place decimal integers may need 2N places. This is true for numbers expressed in any base. In particular, the product of two integers expressed with N-bit binary may need 2N bits. For example, in the picture, two 8-bit unsigned integers are multiplied using the usual paper-and-pencil multiplication algorithm (but using binary arithmetic).

The two 8-bit operands result in a 15-bit product. Also shown is the same product done with base 16 and base 10 notation.


Is a 32-bit general register always able to hold the result of multiplying two 32-bit integers?