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Logic Gate Puzzle
The digital display for a single digit (0 - 9) consists of seven
segments, lit in combinations todisplay the digit. The number is
stored in the calculator as a 4 - bit binary code. For instance,3 =
0011, 5 = 0101, 8 = 1000, etc. The four inputs corresponding to
these binary "bits" areconnected to each of the seven segments by a
combination of gates, so that each segmentlights up only on
combinations of inputs corresponding to those numbers for which it
isrequired.
One of the seven-segment displays in your calculator has become
totally disconnected, andyou open up your calculator. Inside, you
can identify the four inputs A, B, C, D, correspondingto the four
binary bits, and seven loose leads, a - g, each of which should be
connected toone of the segments of the display. For all but one of
the leads, you know the pattern of logicgates between the inputs,
and the output at the lead.
Your task is to work out, for each lead, which binary
combinations will result in an output of'logic 1' at the lead,and
so which segment of the display it should be attached to. Finally,
youwill be left with one lead to attach to the last segment, for
which you do not know the patternof logic gates. Can you work out a
pattern of gates that would make this lead's segment lightup with
the right binary combinations?
Here is the seven - segment display, with its segments lettered
p -v.For each segment, work out which decimal digits 0 - 9 it is
lit for, and which digits it is unlit for.The first one is done for
an example.
00
10
Number in Decimal
Number in Binary:
Inputs: ABCD
0 1 2 3 4 5 6 7 8 9
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001
00
00
00
01
00
11
01
00
01
01
01
10
01
11
10
00
10
01
SEGMENT LIT FOR: UNLIT FOR:
pq
rstuv
0, 2, 3, 5, 6, 7, 8, 9. 1, 4.p
q r
s
t u
v
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The logic gate patterns for the six leads a - f are shown,
togetherwith the 10 combinations ofinputs A - D, representing each
digit. For each lead, work out which binary combinationsresult in
an output of "1", and which give an output of "0". Compare this
with the table you willhave completed above, and work out which
segment p - v it should be connected to.Finally, try to construct a
pattern of gates that will light the last segment correctly with
the lastlead.
Remember:
A
BA
B
A
B
A
BA B
0 0
0 1
1 0
1 1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
AF
A F
0 1
1 0
AND NAND OR NOR
A
B
C
D
Lead "a" Segment:..............0 0 0 00 0 0 10 0 1 00 0 1 10 1 0
00 1 0 10 1 1 00 1 1 11 0 0 01 0 0 1
A B C D Output0123456789
Digit
A
B
C
D
Lead "b" Segment:..............
0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 1
0 1 1 00 1 1 11 0 0 01 0 0 1
A B C D Output
012345
6789
Digit
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A
B
C
D
Lead "c"Segment:..............
A
B
C
D
Lead "d"Segment:..............
Lead "e"
A
B
C
D
Segment:..............
0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 10 1 1 00 1 1 11 0 0 01
0 0 1
A B C D Output
0123456789
Digit
0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 0
0 1 0 10 1 1 00 1 1 11 0 0 01 0 0 1
A B C D Output
01234
56789
Digit
0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 1
0 1 1 00 1 1 11 0 0 01 0 0 1
A B C D Output
012345
6789
Digit
