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# Lab 6

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University of West Florida Electrical and Computer Engineering
Digital Logic and Computer Systems EEL 3701L
Lab 6: BCD to Seven Segment Display Decoder
Due: November 3, 2014

Meghan Szatkowski, Brandon Burrows, Michael Long
Abstract:
For this lab we were to create a circuit that displays decimal numbers from binary numbers since most humans are not capable of reading binary. Using a 7-segment display we are able to achieve that by converting the BCD value into a 7 bit output. The 7-segment display has 7 LEDs and a certain amount of voltage triggers each of the 7 segments to produce a decimal number.

Procedure 1. Create a truth table for your 4 bit input and the corresponding output necessary to light the proper segments of the display. For example, if the input is represented by WXYZ and the output is identified as ABCDEFG then if the input is 0000, all outer LEDs should be lit while the middle LED should be off. Once you create the rows in a truth table for the other 9 combinations, find the function for each segment.

2. Depending on whether you are dealing with more 0s or 1s, choose NAND or AND gates to implement each segment function.

3. Wire the input DIP switches to the decoder input. Note that you have 2 3x8 decoders. You will need to use the inputs and enable lines to combine them in order to implement these 7 functions.

4. Wire the NAND or AND gates to the proper outputs of the decoders in order to implement the functions for each segment.

5. Wire the outputs of the gates to the proper pin on the 7-segment display (refer to the datasheet for the 7-segment display you are using and remember to use a resistor instead of a jumper.

6. Attach 5V to both common anode pins of your 7-segment display (refer to the datasheet for the 7-segment display you are using).

7. Demonstrate number 0-9 to the instructor.

Discussion
For the first part of the lab, a truth table for the 4-bit input and corresponding outputs for the segmented display was created. The truth table can be seen in Table 1 (N is the decimal version of the binary number and the X stands for “don’t cares.”).

WXYZ | a | b | c | d | e | f | g | h | N | 0000 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0001 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0010 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 2 | 0011 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 3 | 0100 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 4 | 0101 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 5 | 0110 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 6 | 0111 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 7 | 1000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 8 | 1001 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 9 | 1010 | X | X | X | X | X | X | X | X | X | 1011 | X | X | X | X | X | X | X | X | X | 1100 | X | X | X | X | X | X | X | X | X | 1101 | X | X | X | X | X | X | X | X | X | 1110 | X | X | X | X | X | X | X | X | X | 1111 | X | X | X | X | X | X | X | X | X |

Table 1. Truth Table.

After the truth table was filled out, the functions for each segment of the display were found. We used the product of sums approach for these functions which can be seen in Table 2. Also, as you can see, h is set to 1 since all of the output are 1.

a | (π 1, 4, 6)’ | b | (π 5, 6)’ | c | (π 2)’ | d | π 0, 2, 3, 5, 6, 8 | e | π 0, 2, 6, 8 | f | π 0, 4, 5, 6, 8, 9 | g | (π 0, 1, 7)’ | h | 1 |

Table 2. Table of functions used in our circuit.
When the functions for the segmented display were found, they were implemented using NAND gates, AND gates, NOT gates, and two 3x8 decoders. First the circuit was built in LogicWorks, as seen in Figure 1, and then tested to make sure that it produced the correct outputs before building the circuit by hand.

Figure 1. The circuit implemented in LogicWorks.

After all the physical wiring was complete, the working circuit was presented to the instructor. The values that were outputted for input values 10-15 were all X since they were “don’t cares,” however we could place values for those “don’t cares” by referring back to our function table (Table 2). Since we used product of sums, the values used for the X would be 1, unless we primed our product of sums function, then the values would be 0. That is because the product of sums includes all the 0 values, meaning the X values would be 1 since they are not listed in our equation. Same goes for our primed product of sums functions; the output for those would be 0, since we used the 1s in our functions, so the rest would be 0. The values of h for 10-15 would be 1 since we set h equal to 1.

WYZX | a | b | c | d | e | f | g | h | 1010 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1011 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1100 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1101 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1110 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1111 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |

Table 3. Don’t care values.

Conclusion This lab proved to be a great way to gain experience with translating binary numbers to decimals numbers on a screen for others to see, since as stated before, most people can’t decipher binary numbers and it also is easier for all to read decimal numbers as well. It puts our foot in the door, for lack of a better expression, for when we learn how to convert binary numbers into letters when that day comes; or for any symbol that would be put on a screen. Wiring the circuit went smoothly, although as you can see from Figure 1, that the circuitry was a little complicated in the sense that there was a lot of wiring to be done and a lot of gates that needed to be used. Needless to say, when we realized that there was a singular gate that could be used for this type of job, we were relieved. However it did show us the basics behind designing a circuit like this. After comparing with other circuit designs, we realized that there could be many ways to implement this specific circuit. Over all, we reached our goal in design a working circuit using a decoder, ANDs, NANDs, and a NOT gate.

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