Question: 1. An unsigned integer x is represented by x mod 256 in some representation scheme. How many bits are allocated for the unsigned integer in

1. An unsigned integer x is represented by x mod 256 in some representation scheme. How many bits are allocated for the unsigned integer in this scheme?

2. For convenience, binary numbers are usually written in hex format. What is AF + F1 in 8-bit unsigned integer representation? Is it overflow?

1. For convenience, binary numbers are usually written in hex format. What is 3F AA in 8-bit unsigned integer representation? Is it overflow?

3. Demote the following 8-bit unsigned integers to 4-bit representation. Indicate if chopping is not possible without losing accuracy.

00000001

10000001

00010001

10001010

10000111

Signed Integer Signed Magnitude Representation

5. What is the largest number in 8-bit sign-magnitude integer representation?

7. What is the smallest number in 8-bit sign-magnitude integer representation?

[see slide 30: same sign addition, opposite sign addition(no overflow possible), subtraction]

9. Calculate the following in 8-bit sign-magnitude integer representation? Indicate if overflow.

01010101 + 00010001	011111100 + 00001111	10011001 + 10101010	11101110 + 11010101
11101111 + 01110001	11110000 + 00111111	11101111 + 01101111	10000000 + 00000000
01010101 - 00010001	01010101 00110011	11011101 - 10101010	11101110 10101010
11101110 + 01110111	11111111 01110111	11101110 - 00110011	11111111 10000000

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