Consider the following 8-bit hexadecimal numbers (the second column). Each of th

Question

Consider the following 8-bit hexadecimal numbers (the second column). Each of these values can be interpreted as an unsigned 8-bit integer or a signed 8-bit integer represented in 2's complement. What is the range of unsigned and signed integers that can be represented using 8 bits? Provide the decimal value for each number and interpretation. Show your work as illustrated in (j). Range of 8-bit unsigned integers:__ Range of 8-bit signed integers (in 2's complement):__ (i) unsigned: 23_16 = 2*16^1 + 3*16 degree = 35_10 signed: 23_16 = 0010.0011_2 this is a positive number; its value is 35.

Explanation / Answer

Range of 8-bit unsigned integers : 0 to (28 -1) = 0 to 255

Range of 8-bit signed integers(in 2's complement) : 0 to 127 (as two's complement can only represent positive integers).

(a) 0xC2

unsigned : C216 = 12 *161 + 2 * 160   = 192 + 2 = 19410

signed : C216 = 1100 0010 => negative number as most significant number is 1

its 1's complement = 0011 1101

2's complement = 1's complement + 1 = 0011 1110 = 62

(b) 0x0A

unsigned : 0A16 = 0*161 + 10 * 160   = 0 +10 = 1010

signed : 0A16 = 0000 1010 => positive number as most significant number is 0, so its value is 10.

(c) 0xEB

unsigned : EB16 = 14 *161 + 11 * 160 = 224 + 11 = 23510

signed : EB16 = 1110 1011 => negative number as most significant number is 1

its 1's complement = 0001 0100

2's complement = 1's complement + 1 = 0001 0101 = 21

(d) 0xCD

unsigned : CD16 = 12 *161 + 13 * 160 = 192+ 13 = 20510

signed : CD16 = 1100 1101 => negative number as most significant number is 1

its 1's complement = 0011 0010

2's complement = 1's complement + 1 = 0011 0011 = 51

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