December
1998 QUESTION 2 Total Marks: 20 Marks |
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| (a) | In the context of floating point numbers, what
is meant by normalisation? Why is this process necessary?
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[3] |
| (b) | Explain carefully why 2's complement format is
used in preference to the older formats of sign-modulus and 1's complement.
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[2] |
| (c) | 2's complement numbers can be multiplied by
powers of 2 using the operation of arithmetic shift left. Explain the
two circumstances in which this operation can cause an overflow to occur.
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[2] |
| (d) | Can the corresponding arithmetic shift right
operation ever cause an overflow? Explain your answer.
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[1] |
| (e) | (i) Show how the hexadecimal number -1.AA16 can be written in normalised floating point format,
with a 10-bit mantissa and a 4-bit exponent.
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[4] |
| (ii) Show how the octal number 1.2628 can be written in the same normalised floating point
format, with a 10-bit mantissa and a 4-bit exponent.
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[4] | |
| (iii) Working in the same floating point format,
perform floating point addition to calculate the sum -1.AA16 + 1.2628 = ... Convert your answer to decimal format |
[4] |