Question

What is the 16-bit hexadecimal representation of each of the following signed decimal integers?

-29

Answer 1

To find the 16-bit hexadecimal representation of -29, calculate the two's complement binary, which is 1110 0011, and then convert those binary digits into hexadecimal, resulting in FFE3.

Step-by-step explanation:

The student is asking for the 16-bit hexadecimal representation of a signed decimal integer, specifically -29. To convert a signed decimal to its hexadecimal representation, we can use two's complement notation. First, we find the two's complement of the absolute value of the number in binary, and then we convert that binary number into hexadecimal.

1. Find the binary representation of 29 (the absolute value of -29): 0001 1101.
2. Invert the digits to get the complement: 1110 0010.
3. Add 1 to the least significant bit to get the two's complement for -29: 1110 0011.
4. Break into 4-bit nibbles and convert to hexadecimal: E3.

So, the 16-bit hexadecimal representation of -29 is FFE3, since we need to fill the rest of the bits to make it 16-bit with 'F's to represent that it is a negative number in two's complement notation.

Answer 2

FFE3

Step-by-step explanation:

The 16 bit binary representation of 29 = 0000000000011101

The corresponding hexadecimal representation = 001D

Taking 2s complement, the binary representation of -29:

Step 1 : 1's complement of 29 = 1111111111100010

Step 2 : Adding 1 to 1's complement to get the 2's complement => 1111111111100010 + 1

= 1111111111100011

Converting the binary representation to equivalent hexadecimal format: FFE3