Question

Signed values: Convert each as indicated. You do not need to show your work. (But please do some explain,thanks)

If the answer must be a byte, then it must be the correct size.

1. Hexadecimal to decimal (signed magnitude)

1. 0x86
2. 0xE9

2. Hexadecimal to decimal (1’s complement)

1. 0x86
2. 0xE9

3. Hexadecimal to decimal (2’s complement)

1. 0x86
2. 0xE9
3. 0x14

Answer 1

in order to convert any number to the decimal form

the magnitude of the number *base of the number^{(position of the number)} additio of all possible spaces gives us the corresponding decimal number

for example

a.)

(86)₁₆ is an hexadecimal number with base 16

now

8*16¹+6*16⁰(this will give us the decimal)

=128+6=134 (unsigned)

now in order to see if the number is negative, we need a binary representation (is MSB is one for signed number the number is negative else it's positive

a signed number have n-1 number of bit since MSB defined the sign

now, 0x86 in binary=1000(8)0110(6)=10000110= -6 in decimal since MSB is 1 and magnitude is 6

now doing the same for part b.)

E9

unsigned 14*16¹+9*16⁰=233

binary representation 1110(E)1001(9)=11101001= -105

now 1's complement

when a negative number is present all the bits of the number are inverted 0 to 1 and 1 to 0 respectively

1's complement for 86 hex

will be

an invert of signed binary 10000110

01111001 =121

for E9

an invert of signed binary11101001

00010110=22decimal

now for 2's complement adding 1 to the LSB of the 1's complement of a negative number gives the corresponding 2;s complement

for 86

01111001+00000001=01111010=122

for E9

00010110+00000001=00010111=23

for 0x14

binary 0001(1)0100(4)=00010100 since the number is not a negative number since MSB =0 no need for an 2's complement

representation.