Description
even Segment Circuit Design
Design a circuit that correctly shows the numbers 0-7 on a seven segment display
given a 3-bit binary input.
deliverables: You will turn in 2 items. The 1st file should be named
sevenSegment.circ and contain your circuit implemented in logisim; submit this file
to Moodle. The 2nd part should contain your truth table, karnaugh maps, and
boolean expressions from steps 1-3 below. You may submit this as an electronic file
or turn it in on paper at the beginning of class Wednesday (or put it in my mailbox
anytime before that.
A seven-segment display is a familiar output device that is used to display numbers
and a few letters. Simple alarm clocks, old calculators, and lots of other devices use
seven-segment displays. Logism has a seven-segment display widget in its
Input/Output section. Your job is to create a Logisim circuit taking three input lines
representing an integer between 0 and 7 (each input is 1 bit of a 3-bit binary
number), and produce output on a seven-segment display widget showing the
corresponding digit. You may use AND, OR, and NOT gates, plus necessary pins and
wires. The diagram below shows how the inputs to the Logisim seven-segment
display correspond to the 7 segments. If an input is 1, the corresponding segment
will be turned on. The 8th input connects to an optional decimal point that can light
up, but we will ignore that.
You will complete this in the following steps:
1. Make a truth table showing the value of each segment (1 meaning on and 0
meaning off) for each 3-bit input. Use the following format for each number.
For example, the first row would look like
x0 x1 x2 seg1 seg2 seg3 seg4 seg5 seg6 seg7
0 0 0 0 1 1 1 1 1 1
2. Create a karnaugh map for each segment, and circle or somehow mark the
groups of 1’s. Note that the segments are completely independent, you are
basically creating 7 different circuits using the same 3 inputs, 1 for each
segment. The completed truth table for seg1 is
x0 x1 x2 seg1
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
which gives the karnaugh map
3. Use the karnaugh map to write out a simplified boolean algebraic expression
for each segment. For the above map I get the following expression
representing seg1
Note that there may be multiple equivalent expressions for a segment that
are equally simple. For example on the above map I could have circled the 1’s
in the lower left & right corners instead of the last column, giving the
expression
Any one of these equivalent expressions are acceptable.
4. Finally use your 7 expressions to create your circuit in logisim. Your final
circuit should be clean and easy to interpret. Note that you can choose
between 3 sizes of each gate in logisim to help make this easier. Below is a
circuit for seg1, you should add the other 6 circuits in a column below seg1 as
shown in the diagram, using the same inputs (you will need to extend the
input lines further down).
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