Seven 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).

Sale!