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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