Multiplication with binary unsigned numbers

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SUMMARY

The discussion centers on the multiplication of binary unsigned numbers, specifically the operation 1111010 (which is -122 in 2's complement) multiplied by 1001 (which is -9 in 2's complement). The result of this multiplication is incorrectly calculated as 0001001010, leading to confusion regarding the sign of the outcome. It is clarified that the leftmost bit in binary representation indicates the sign in 2's complement notation, and the correct interpretation of the bits is crucial for accurate calculations. The importance of knowing the number of bits used in the representation is emphasized to avoid misinterpretation of negative and positive values.

PREREQUISITES
  • Understanding of 2's complement representation
  • Knowledge of binary arithmetic
  • Familiarity with signed and unsigned numbers
  • Experience with bit manipulation techniques
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  • Study 2's complement arithmetic in detail
  • Learn about binary multiplication algorithms
  • Explore the implications of bit length in binary operations
  • Research the differences between signed and unsigned binary numbers
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Students, software engineers, and computer scientists interested in binary arithmetic, particularly those working with low-level programming or digital systems design.

shamieh
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1111010 x 1001 is a negative * a negative so I should get a positive right?

which I got 0001001010.

BUT, if it's -122 x -9 = 1098. How come I get a positive number that doesn't equal 1098. Aren't you supposed to disregard the most left bit if it's more numbers than your original like wouldn't i disregard the 1 carry in 10001001010, because if I included it in the answer wouldn't that make it -122 * -9 which = -1098. And how is that possible.
 
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shamieh said:
1111010 x 1001 is a negative * a negative
Why are you saying that? First, are you talking about 2's complement? Second, what number of bits do you have? Only when you know the number of bits, you can say which numbers are negative in 2's complement: the leftmost bit must be 1. But the leftmost bit here means that you have to use all bits, even if this means leading zeros. For example, if you have 8 bits, then 1001 is 00001001, the leading bit is 0 and the number is positive.
 

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