In this tutorial, we continue from where we left off in the previous lesson. Last time, we derived the Boolean expression for output A of our 7-segment display using the Sum of Products (SOP) method. Today, we will extend that process to all the remaining outputs (B, C, D, E, F, and G) and prepare everything for building the full schematic in Multisim.

If you’re new here, remember: a 7-segment display has seven outputs (a, b, c, d, e, f, g) that control the individual LED segments. By turning specific outputs ON or OFF, we can display numbers (0–9) or even some letters.



Recap: Output A Expression

Previously, we derived the Boolean expression for segment A from the truth table. The method we used was the Sum of Products (SOP):

  • We circled all the 1’s in the truth table for output A.

  • For each “1,” we wrote down the corresponding product term (with complemented inputs represented as ’ or dash).

  • Finally, we summed (added) all the product terms to form the Boolean expression.

This exact same process will now be repeated for outputs B–G.


Step 1: Boolean Expression for Output B

Following the SOP method:

  1. Circle all the 1’s in the B column of the truth table.

  2. Write down the product terms for each 1.

    • Example: If inputs are A=0, B=0, C=0, D=1 → the product is A’B’C’D.

  3. Add all the product terms with a “+” sign.

The final Boolean expression for output B looks like this:

B = A’B’C’D + A’B’CD’ + A’BC’D’ + A’BCD + AB’C’D + AB’CD’

Step 2: Boolean Expression for Output C

Repeating the same method for output C:

C = A’B’C’D’ + A’B’CD’ + A’BCD + AB’C’D’ + AB’CD

Step 3: Boolean Expression for Output D

For output D, we circle the ones, write product terms, and combine them:

D = A’B’C’D’ + A’B’CD’ + A’BCD’ + A’BCD + AB’C’D’ + AB’CD

Step 4: Boolean Expression for Output E

The Boolean expression for output E becomes:

E = A’B’C’D’ + A’B’CD’ + A’BCD’ + AB’C’D’

Step 5: Boolean Expression for Output F

For output F, the Boolean expression is:

F = A’B’C’D’ + A’BC’D’ + A’BCD + AB’C’D’ + AB’CD

Step 6: Boolean Expression for Output G

Finally, the Boolean expression for output G:

G = A’B’C’D’ + A’B’CD’ + A’BCD’ + A’BCD + AB’C’D’ + AB’CD

Step 7: Building Schematics in Multisim

Now that we have all seven Boolean expressions (A through G), the next step is to:

  1. Open Multisim.

  2. Create a circuit for each Boolean expression using AND, OR, and NOT gates.

  3. Connect each circuit to its corresponding 7-segment display pin:

    • Segment A → Output A

    • Segment B → Output B

    • …and so on through G.

At the end, we will have a fully functional 7-segment display driver built entirely from Boolean expressions and logic gates.


Going Beyond: Displaying Numbers with Multiple 7-Segment Displays

So far, we’ve built the logic for a single 7-segment display. But what if we want to show two-digit or three-digit numbers like 98 or 123?

  • Each 7-segment display requires its own set of inputs (A, B, C, D).

  • To show 98, for example:

    • The first display gets the input 1001 (which corresponds to 9).

    • The second display gets the input 1000 (which corresponds to 8).

This way, by combining multiple 7-segment displays, we can represent numbers from 00 to 99, or even 000 to 999 if we use three displays.


Conclusion

In this tutorial, we:
✔ Derived Boolean expressions for all 7 outputs (A–G) of a 7-segment display.
✔ Learned how to implement them using the Sum of Products (SOP) method.
✔ Prepared the expressions for schematic design in Multisim.
✔ Discussed how multiple 7-segment displays can be used to show multi-digit numbers.

In the next tutorial, we’ll move into Multisim simulation, build the actual circuits for each segment, and test our design with inputs 0000 through 1001 (0–9).

Stay tuned — by the end, you’ll have a complete 7-segment display driver designed from scratch!