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Check, using complementary code rules, if:

  • if $(9A7D)_{16}$ and $(7583)_{16}$ are complementary in a location of $2$ bytes
  • if $(000F095D)_{16}$ and $(FFF0F6A3)_{16}$ are complementary in a location of 4 bytes

I am not sure what the problem statement means exactly. What am I supposed to check? In the case of the first subpoint, I converted the two numbers into binary to see if they are complementary over a location of $16$ bits ($2$ bytes). Again, I have no idea if I am supposed to do this.

$$ (9A7D)_{16} = 1001 \hspace{0.1cm} 1010 \hspace{0.1cm} 0111 \hspace{0.1cm} 1101 _ {2} $$

$$ (7583)_{16} = 0111 \hspace{0.1cm} 0101 \hspace{0.1cm} 1000 \hspace{0.1cm} 0011 _ {2} $$

But in order for the two to be complementary in a location of $2$ bytes we would need the two numbers to be complementary as a whole, since the whole number representations have $2$ bytes. This looks to be false. The second subpoint of the problem reaches the same conclusion. This is what I don't think that it's right what I'm doing. It doesn't feel like I did much. So what exactly is the problem statement asking for?

1 Answers1

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The problem is asking to check the two values using 1's complement and 2's complement rules.

To calculate 1's complement, subtract each digit from $15\space(=F_{16})$.

To calculate 2's complement, add 1 to one's complement.

$1$'s complement of $9A7D_{16} = 6582_{16}$ and not $7583_{16}$

$2$'s complement of $9A7D_{16} = 6582_{16} + 1 = 6583_{16}$ which is also not $7583_{16}$.

So, the values are neither one's complements not two's complements of each other.

Repeat the same for the 4 byte value. A cursory check shows they are 2's complements of each other.

vvg
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  • Can you please clarify something for me? So, in order to find $1$'s complement we take the largest value in the given base and subtract each digit from that largest value (e.g., $15$ in base $16$, $1$ in base $2$, $9$ in base $10$, and so on)? Also isn't the first digit of $1$'s complement in the exercise you solved actually $6$ and not $7$? I might be wrong, but you said to subtract each digit from 15, so we would have $15 - 9 = 6$. Am I wrong? –  Oct 01 '20 at 10:41
  • Yes. That is correct. I made a math error in the first digit. My bad. So, they are not 1's or 2's complements for the first answer. But the rules are correct. – vvg Oct 01 '20 at 10:52