Consider the following 8bit hexadecimal numbers the second c

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.

Solution

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