According to this Wikipedia article, when arithmetic left shift operation is applied to a signed number, the number is multiplied by 2. But there are certain situations where a negative number becomes a positive number when an arithmetic left shift is applied.

Eg.: Take a 2's complement signed integer -5 and 5 bits are used to represent it.

11011 ==> -5
10110 ==> -10 (-5x2)
01100 ==> +12 (?)

So after two arithmetic left shifts -5 became 24. I expected -20. Why is this the case?

  • $\begingroup$ Please explain how you would store -20 in a 5 bit signed integer. $\endgroup$
    – gnasher729
    Aug 22, 2019 at 17:33

1 Answer 1


$01100 \Rightarrow +12$, not $+24$.

And it is $+12$ because $32-20=12$. With $5$ bits and $2$s complement you can only represent numbers in the range $-16$ to $+15$. You have overflowed this range and, in effect, "run around" to the other end and into the positive number range.


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