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What is the equivalent 2's complement representation for -15 in 16-bit hexadecimalrepresentation?a FFFEb) 7FFEc) FFF1d) 7FF1

Question
What is the equivalent 2's complement representation for -15 in 16-bit hexadecimal
representation?
a FFFE
b) 7FFE
c) FFF1
d) 7FF1
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What is the equivalent 2's complement representation for -15 in 16-bit hexadecimal representation? a FFFE b) 7FFE c) FFF1 d) 7FF1

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Step 1

For representing –15 in 2’s complement notation following steps should be followed:

  1. Find the binary equivalent of 15.
  2. Represent the equivalent binary representation using 16 bits.
  3. Use the most significant bit for sign representation.
  4. Get 2’s complement of the above binary representation.
  5. Convert the obtained 2’s complement representation in hexadecimal form.
Step 2

Now,

The number 15 in binary form is represented as 1111. In 16-bit representation the number 15 will be represented as 0000 0000 0000 1111.

Now make the most significant bit of above decimal number as 1 since the number is negative. Therefore, –15 in 16-bit decimal representation will be represented as 1000 0000 0000 1111.

Step 3

Now to find the 2’s complement of the 16-bit representation of above number first find the 1’s complement and then add 1 to the result to obtain 2’s complement.

Now, 1’s complemen...

0111 1111111 0000
1
0111111111 0001
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0111 1111111 0000 1 0111111111 0001

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