[Math] Where do we place the decimal point due to a binary multiplication of two decimal binary numbers

binarybinary operations

An example can be $$ 0010000.010 * 0001000.010 $$ which will give $$1000110.000100$$

But how was the operation done? More precisely, how was the decimal point placed there?
Is the rule for placing the decimal point in the previous example exclusive for that example because the two numbers have equal number decimal places (3) ? or there is a general rule for placing the decimal point whether or not the number of decimal places are the same? (like will the rule you'll provide me still apply when multiplying 1011 * 0.010 ?
Kindly place all zeros even the useless ones (after the last non-zero digit in the decimal part).

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Best Answer

From DelightfulyLinux blog post:

Multiplying Binary Fractions

Align both rows by the least significant bit and multiply the same way as in decimal multiplication. The final position of the radix point is the sum of the number of radix point places from both factors.

That is why in your example final result has 6 bits in fractional part - because the sum of the fractional bits from both operands is $$ 3+3=6 $$

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