Integer Representations Write the hexadecimal representation

Integer Representations. Write the hexadecimal representation of the word 1111 1101 1011 1001 0111 1010 0011 0001_two For the word 0000 0000 0000 0000 0000 0000 0000 0011two what decimal (base 10) number does it represent, assuming that it is an unsigned integer? For the word 0000 0000 0000 0000 0000 0000 0000 0011two what decimal (base 10) number does it represent, assuming that it is a two\'s complement integer? For the word 1111 1111 1111 1111 1111 1111 1111 1111two what decimal (base 10) number does it represent, assuming that it is a two\'s complement integer?

Solution

1. 1111 1101 1011 1001 0111 1010 0011 0001₂

= F D B 9 7 A 3 1

2. 0000 0000 0000 0000 0000 0000 0000 0011₂

= 2⁰ + 2¹ = 1 + 2 = 3₁₀.

3. 0000 0000 0000 0000 0000 0000 0000 0011₂

1\'s complement of this number is: 1111 1111 1111 1111 1111 1111 1111 1100.

And adding 1 to this will make it 2\'s complement of the original number.

Therefore, 2\'s complement of the original number is: 1111 1111 1111 1111 1111 1111 1111 1101.

As, the Most Significant Bit is 1, which means, its a negative number.

Therefore, the number is: 2⁰ + 2² + 2³ + 2⁴ + ... + 2³⁰ = -2147483645₁₀.

4. 1111 1111 1111 1111 1111 1111 1111 1111₂

1\'s complement of this number is: 0000 0000 0000 0000 0000 0000 0000 0000.

And adding 1 to this will make it 2\'s complement of the original number.

Therefore, 2\'s complement of the original number is: 0000 0000 0000 0000 0000 0000 0000 0001.

As, the Most Significant Bit is 0, which means, its a positive number.

Therefore, the number is: 2⁰  = 1₁₀.