08 Jun Computer Archtecture : Data representation
Question
1. What Decimal value does the 8-bit binary number 10011110 have if:
A. It is interpreted as an unsigned number?
B. It is on a computer using signed-magnitude representation?
C. It is on a computer using one’s complement representation?
D. It is on a computer using two’s complement representation?
2. Assume we are using the simple model for floating-point representation as given in this boon (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 16, a normalized mantissa of 8 bits, and a single sign bit for number):
A. Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format.
B. Show how the computer would add the two floating-point numbers in “Part A” by changing one of the numbers so they are both expressed using the same power of 2.
C. Show how the computer would represent the sum in “Part B” using the given floating point representation. What decimal value for the sum is the computer actually storing?
Explain:
3. Show how each of the following floating point values would be stored using IEEE-754single precision (be sure to indicate the sign bit, the exponent, and the significant fields):
A. 12.5
B. -1.5
C. 0.75
D. 26.625
4. Find the quotients and remainders for the following division problems modulo 2.
A. 1111010 / 1011
B. 1010101 / 1100
C. 1101101011 / 10101
D. 1111101011 / 101101
5. Using CRC polynomial 1101 compute the CRC code word for the information word 01001101.
Check the Division performed at the receiver.
6. A 15-bit floating point number has 1 bit for the sign of the number, 5 bits for the exponent and 9 bits for the mantissa (which is normalized). Numbers in the exponent are in signed magnitude representation.
No bias is used and there are no implied bits.
Show the representation for the smallest positive number this machine can represent.
0 11111 100000000
Sign Exponent Mantissa
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