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# Digital Logic Worked Example: Schematic to Function

Module by: Kiran Pathakota, Ayana Andalcio. E-mail the authorsEdited By: Elec and Comp 326

Summary: This is a worked example demonstrating how to obtain the function from a given transistor level schematic.

In the following exercise, a transistor level schematic will be analyzed and it's underlying function will be found.

## Exercise 1: Schematic to Function

Fill out the truth table for the following mystery schematic (Fig 1) and determine the function.

### Solution

#### Working It Out

1. Step 1: Look at the schematic and determine how the bit values travel through the gates.:

Note that this is a valid schematic and that the p-MOS transistors are connected to the ground and the n-MOS transistors are connected to Vdd

.
2. Step 2: Construct the input section of the truth table to contain all possible combination of inputs.: .
3. Step 3: Apply each combination of inputs to the schematic to determine the flow of bit values to Y: Complete the truth table with the corresponding output Y to its input .
4. Step 4: Write the output equation as either a Product of Sums or Sum of Products :

Y = A'B'C + A'BC' + AB'C' + ABC OR Y = (A' + B' + C').(A' + B + C).(A + B' + C').(A + B + C')

.
5. Step 5: Simplify the output equation to determine the function of the mystery schematic:

Also, try to notice patterns that you have already learned about. Clearly, the output is high only when there is an odd number of inputs high. Thus, we can conclude that this is a 3 - input XOR.

Answer: Y = XOR(A, B, C)

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