How do I design a BCD to seven-segment decoder using a single decoder and OR gates only?

Where,
The desired decimal digit is expressed in binary-coded-decimal (BCD) format, and then used as an input to a logic network which controls the seven segments.

For this project, you will develop a multiple-output logic network that drives a 7-segment display, yielding all ten decimal digits. Here is how you will proceed:

1. The input variables will be the BCD representations of the decimal digits 0-9 (use switches 0-3 on your board: SW0= LSB, SW3= MSB).

2. Using Karnaugh maps, determine the seven output functions for controlling each of the seven segments, in minimum SOP form. Using Don't Cares will greatly simplify your output functions.

3. Express the seven output functions

4. You will display the digit on the left 7-segment digit on your board. Refer to the manuals regarding how to enable a specific digit on this display. Hint: Applying a logic low level to a segment causes it to light up and applying a high level turns it off.

Respuesta :

Truth Table:

let A = SW3, B = SW2, C = SW1, D = SW1

1. The truth table is attached in mage below. abcdefg are the 7 outputs of seven segment display.

2. K-maps of all 7 outputs is also attached as image to this response.

3. Outputs of seven segment display as SOP are as follows =

a = ~B~D + C + BD + A

b = ~B + ~C~D +CD

c =  ~C +D +B

d = ~B~D + ~BC + B(~C)D + C(~D) + A

e =  ~B~D + C~D

f =  ~C~D + B(~C) +B(~D) + A

g =  ~BC + B(~C) + A + B(~D)

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