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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).
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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.
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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.
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[4] |
| (e) |
Draw a circuit to implement the simplified SOP expression. |
[3] |
from
a 4-bit counter, and produces twenty outputs 
,
one for each light bulb.
,
the top left bulb in the display.
