Seven-segment displays are very common output display devices that are used in many common application like clocks, radios, calculators, odometers, etc. It is one of the easiest way to implement a numeric output for a digital circuit for a hexadecimal base. It takes a four-bit binary numeric input, and uses a display made of seven long, thin LEDs arranged in a parttern of an eight to create to signals necessary to drive the display. If we label the seven LEDs as (a, b, c, d, e, f, g), these seven outputs of the decoder select the corresponding segments in the display, as it shown below:

Do the following:

1. (a) Drive the truth table for a circuit which will control LED segment ”c” of a seven-segment display. For example, for number 0, 1, 3, your LED representing ”c” should light up, whereas for numbers such as 2, E, or F it should not.

2. (b) Use Karnaugh map reduction to get a simplified Boolean function design for a seven-segment decoder that uses a minimum number of gates in sum-of-product form. Implement your circuit in the simulator, using only NAND and NOT gates.

3. (d) Verify that it matches the truth table found in (a). In your implementation, also use seven-segment display and connect directly to your inputs to compare your result from LED to what is shown on the seven-segment display. Remember that the seven-segment display also has a ground input that needs to be connected. please including the screenshots of the implementation in (c) with at least two different set of inputs in which the segment ”c” is on and off.

Please answer the question b) completely, it is to design the circuit for the whole seven segment, not just for c, and provide the implementation with Logisim

 

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