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# Digital Logic Worked Example: Daryl's Discombobulation

Module by: Elaine Chung, Isiana Rendon Escarcega, Daryl Arredondo. E-mail the authorsEdited By: Elec and Comp 326

Summary: Worked examples on understanding truth tables with Daryl Arredondo.

## Daryl's Big Day!

### Exercise 1: Daryl's First Challenge

Daryl Arredondo wants to create a three-input "minority" gate, which produces a TRUE output if and only if fewer than half of the inputs are true. Draw a truth table for Daryl's gate.

#### Solution

Fill out the truth table by putting a 1 in the output column whenever at least two inputs are 0.

 A B C Y 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0

### Exercise 2: Daryl's Final Battle

Daryl Arredondo wants to create a Boolean function with 5 variables. How many possible truth tables could he draw for a Boolean function of 5 variables?

#### Solution

The number of possible input combinations is 25 2 5 because each variable can be either 0 or 1. The output of each combination can be either 0 or 1, so the total number of possible truth tables is 225=4294967296 2 2 5 4294967296 .

### Exercise 3: Daryl's Happy Ending

Daryl Arredondo is indecisive and decided to create a Boolean function with n variables instead. Generalize the result from the previous question to determine how many truth tables he could draw for a Boolean function of n variables.

#### Solution

He could draw 22n 2 2 n truth tables.

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