Consider the following 16-bit hexadecimal numbers (the second column). Each of t

Question

Consider the following 16-bit hexadecimal numbers (the second column). Each of these values can be interpreted as interpreted as an unsigned 16-bit integer or a signed 16-bit integer represented in 2's complement. What is the range of unsigned and signed integers that can be represented using 16 bits? Range of 16-bit unsigned integers: _0 to 65, 535____ Range of 16-bit signed integers (in 2's complement): -32, 768 to 32, 767 _____ Provide the decimal value for each number and interpretation. Show your work as illustrated in (i).

Explanation / Answer

1. (81C2)16 = 8*163 + 1*162 + 12*161 + 2*160 = (33218)10
Signed Number : 81C2 = 1000 0001 1100 0010 ==> negative number
Twos complement is : 0111 1110 0011 1110 => (7E3E)16 =>(0111111000111110)2 = (-32318)10

2. (B607)16 = 11*163 + 6*162 + 0*161 + 7*160 = (46599)10
Signed Number : B607 = 1011 0110 0000 0111 ==> negative number
Twos complement is : 0100 1001 1111 1001 => (49f9)16 =>(0100100111111001)2 = (-18937)10

3. (39CD)16 = 3*163 + 9*162 + 12*161 + 13*160 = (14797)10
Signed Number : 39CD = 0011 1001 1100 1101 ==> Positive number
Twos complement is : 0011 1001 1100 1101 => (39CD)16 =>(0011 1001 1100 1101)2 = (14797)10

4. (0012)16 = 0*163 + 0*162 + 1*161 + 2*160 = (18)10
Signed Number : 0012 = 0000 0000 0001 0010==> Positive number
Twos complement is : 0000 0000 0001 0010 => (0012)16 =>(0000 0000 0001 0010)2 = (18)10

Thanks, let me know if there is any concerns.

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