August
1999 QUESTION 3 Total Marks: 20 Marks |
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| A water heater is
controlled by a device D that monitors four sensors W, X, Y , Z. If sensors W and Z both
signal 1, then device D should be on; otherwise, if sensor W signals 0 to sensor Y signals
1, then D should be off; otherwise, if sensors W, X, Y all signal 1, then D should be on;
otherwise, if sensor W signals 1 and sensor Z signals 0, then D should be off; otherwise
we don't care what the device does.
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| (a) | Give the truth-table for device D.
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[3] |
| (b) | Give an unsimplified sum-of-products
expression for the device D.
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[1] |
| (c) | Using a Karnaugh map, find the simplified
sum-of-products and product-of-sum forms of this expression.
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[7] |
| (d) | Draw a circuit to implement the simplified
sum-of-products above, using AND, OR and NOT.
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[3] |
| (e) | Express the simplified sum-of-products form
from part (c) using only NAND, and hence redraw the circuit using only NAND gates.
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[4] |
| (f) | Why might the circuit in part (e) be
preferable to the circuit in part (d)? What does this mean for the skills of a circuit
designer?
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[2] |