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In preparation for the Year 2000 celebrations, you are to design a controller for an electronic ‘marquee’ banner. The banner will show the message “2000”:
(The larger circles indicate lit bulbs.) The display will consist of twenty light bulbs, arranged in a rectangle of width 4 and height 5. It will cycle through 16 phases, displaying a horizontally-scrolling ‘window’ onto the above message. Thus, in phase 0 the bulbs show columns 1 to 4 of the message (as in Figure 1 below). In phase 1, the message scrolls one place left, so the bulbs show columns 2 to 5 of the message (Figure 2). The next three phases are shown in Figures 3 to 5.
The light bulbs are operated by a controller.
This controller takes four inputs
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| (a) |
Complete this truth table for the control
for bulb
(Here, a ‘1’ in the last row indicates
that the bulb should be lit).
(Full marks for a completely correct table; 1 mark if there is just one mistake; no marks if there are more mistakes.)
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[2] |
| (b) |
Give an unsimplified sum-of-products
expression for
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[2] |
| (c) |
Simplify this SOP expression, using a
Karnaugh map.
and so
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[4] |
| (d) |
Use boolean algebra to derive a product-of-sums
expression for the negation of the above simplified sum-of-products
expression. State the laws used.
(1 mark for each
correct step (to a maximum of 2 marks), 1 mark for naming the law(s)
used, 1 mark for obtaining the correct answer. Award a maximum of
3 marks if they derive the POS expression
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[4] |
| (e) |
Draw a circuit to implement the simplified
SOP expression.
(1 mark for each AND gate correctly connected; 1 mark for clear labelling. Watch for consequential error, if they got the SOP expression wrong.) [3 marks] |
[3] |
from
a 4-bit counter, and produces twenty outputs 
,
one for each light bulb.
,
the top left bulb in the display.
(1, 2, 3, 6, 10, 14) (Full marks for a completely correct expression;
1 mark if there is just one mistake; no marks if there are more mistakes.)
.
(1 mark for each correct block in the map, 1 mark for each correct
term in the simplified expression. Watch for consequential error,
if they got the SOP expression from the previous part wrong.) [4 marks]
for
the ones instead of the expression for the zeroes. Watch for consequential
error, in case they got the simplified SOP expression wrong.) [4 marks]
