1 - [2 pts] Briefly describe overflow. When does it occur? 2 - [2 pts] Briefly d
ID: 3848336 • Letter: 1
Question
1 - [2 pts] Briefly describe overflow. When does it occur?
2 - [2 pts] Briefly describe underflow. When does it occur?
3 - What decimal number does the bit pattern 11000101 represent if it is a: • [1 pts] unsigned integer? • [1 pts] sign-magnitude integer? • [1 pts] two's complement integer?
4 - What decimal number does the bit pattern 01011100 represent if it is a: • [1 pts] unsigned integer? • [1 pts] sign-magnitude integer? • [1 pts] two's complement integer?
5 - [2 pts] What is the binary representation of the decimal number 6.5 assuming the IEE 754 single precision format?
6 - What decimal number does the bit pattern 0xC3A80000 represent if it is: • [2 pts] A two's complement integer? • [2 pts] An unsigned integer? • [2 pts] A floating point number assuming the IEE 754 single precision format
7 - [3 pts] If the bit pattern 0x8CF00000 is loaded into the instruction register, what is the name and type of the assembly language instruction that will be executed?
8 - Perform the following calculations assuming that the values are 8-bit decimal integers stored in two's complement format. • [2 pts] 10101010 + 01101101 • [2 pts] 10101001 - 01101111
Explanation / Answer
1.
In computer programming, an overflow occurs when the result of an arithmetic operation is a numeric value that is outside of the range (that requires more bits to be represented) – either larger than the maximum or lower than the minimum representable value.
2.
Underflow occours when the result is so small that it cannot be stored, i.e. its magnitude is smaller than the smallest possible value representable as a normal floating point number in the target datatype.
3.
number: 11000101
Sign Magnitude:
Sign: 1 i.e. minus
Magnitude: 1000101 is 69;
So the value is -69
1's Complement:
Sign: -ve since MSB is 1
magnitude: 00111010(invert 0's and 1) is 58
So value = -58
2's Complement
Value is: -59
-1*27 + 1*26 + 1*22 + 1*20 = -128 + 64 + 4 + 1
4.
number: 01011100
Since the number does not contain a leading 1 (i.e. MSB is 0) the number is not a -ve number and represents same value in all 3 number system. The value is: 1*26 + 1*24 + 1*23 + 1*22 = 64 + 16 + 8 + 7 = 92
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