ENG_274_Lab_Report_Lab_2

ENG_274_Lab_Report_Lab_2 - Lab 2 Report Binary to 7-segment...

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Lab 2 Report: Binary to 7-segment LED Decoder Student Information: Jonathan Sooter [email protected] Partner: Corey Davis Lab Purpose: The purpose of this lab was to create a module that takes 4 binary inputs and outputting their hexadecimal representation on a 7-segment LED display. It was also designed to help familiarize us with the 7-segment LED display and re-enforce what we've learned about boolean algebra. Implementation Details: The pre-lab assignment was to create a truth table and corresponding Boolean equations implementing the desired functionality of the binary to 7-segment LED Decoder so the first thing I did was generate this truth table: O I 3 I 2 I 1 I 0 A B C D E F G 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 2 0 0 1 0 1 1 0 1 1 0 1 3 0 0 1 1 1 1 1 1 0 0 1 4 0 1 0 0 0 1 1 0 0 1 1 5 0 1 0 1 1 0 1 1 0 1 1 6 0 1 1 0 1 0 1 1 1 1 1 7 0 1 1 1 1 1 1 0 0 0 0 8 1 0 0 0 1 1 1 1 1 1 1 9 1 0 0 1 1 1 1 1 0 1 1 A 1 0 1 0 1 1 1 0 1 1 1 b 1 0 1 1 0 0 1 1 1 1 1 C 1 1 0 0 1 0 0 1 1 1 0 d 1 1 0 1 0 1 1 1 1 0 1 E 1 1 1 0 1 0 0 1 1 1 1 F 1 1 1 1 1 0 0 0 1 1 1
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After the truth table was completed I wrote the equation for each segment A through G as the sum-of-minterms. This resulted in 6 very long equations that follow: A = I3'I2'I1'I0' + I3'I2'I1I0' + I3'I2'I1I0 + I3'I2I1'I0 + I3'I2I1I0' + I3'I2I1I0 + I3I2'I1'I0' + I3I2'I1'I0 + I3I2'I1I0' + I3I2I1'I0' + I3I2I1I0' + I3I2I1I0 B = I3'I2'I1'I0' + I3'I2'I1'I0 + I3'I2'I1I0' + I3'I2'I1I0 + I3'I2I1'I0' + I3'I2I1I0 + I3I2'I1'I0' + I3I2'I1'I0 + I3I2'I1I0' + I3I2I1'I0' C = I3'I2'I1'I0' + I3'I2'I1'I0 + I3'I2'I1I0 + I3'I2I1'I0' + I3'I2I1'I0 + I3'I2I1I0' + I3'I2I1I0 + I3I2'I1'I0' + I3I2'I1'I0 + I3I2'I1I0' + I3I2'I1I0 + I3I2I1'I0 D = I3'I2'I1'I0' + I3'I2'I1I0' + I3'I2'I1I0 + I3'I2I1'I0 + I3'I2I1I0' + I3I2'I1'I0' + I3I2'I1'I0 + I3I2'I1I0 + I3I2I1'I0' + I3I2I1'I0 + I3I2I1I0' E = I3'I2'I1'I0' + I3'I2'I1I0' + I3'I2I1I0' + I3I2'I1'I0' + I3I2'I1I0' + I3I2'I1I0 + I3I2I1'I0' + I3I2I1'I0 + I3I2I1I0' + I3I2I1I0 F = I3'I2'I1'I0' + I3'I2I1'I0' + I3'I2I1'I0 + I3'I2I1I0' + I3I2'I1'I0' + I3I2'I1'I0 + I3I2'I1I0' + I3I2'I1I0 + I3I2I1'I0' + I3I2I1I0' + I3I2I1I0 G = I3'I2'I1I0' + I3'I2'I1I0 + I3'I2I1'I0' + I3'I2I1'I0 + I3'I2I1I0' + I3I2'I1'I0' + I3I2'I1'I0 + I3I2'I1I0' + I3I2'I1I0 + I3I2I1'I0 + I3I2I1I0' + I3I2I1I0 These 7 equations would give the desired functionality that the lab is looking for but I don't like having those giant equations so I started to simplify the equations using the properties of Boolean algebra. I ended up with these, equivalent and much shorter, 7 equations: A = I3'(I2I0 + I1) + I3(I2'I1' + I0') + I2I1 + I2'I0' B = I0'(I3'I1' + I2') + I0(I3 ^ I1) + I3'I2' C = (I3 ^ I2) + I1'I0 + I3'(I0 + I1') D =
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