Digital Logic Design

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Questions

1. Describe the behavior of the CMOS circuit shown in the ?gure below, clearly indicating for what values of x and y the transistors conduct.

2. Convert the following English problems to Boolean Equations. Introduce Boolean variables as needed:

"An automatic car brake should stop the car when the auto-brake system is enabled andneither handbrake or manual car brake are extended."3. Evaluate the Boolean equation F = a AND (b OR (c AND d)) for the given values of a,b,c,d:

1. a = 1, b = 1, c = 0 , d = 1

2. a = 1, b = 0, c = 0, d = 0

4. Convert the following Boolean equation into a gate-level circuit F = [(x'y)(x'+z)]'

5. Design an irrigation system controller circuit that opens the sprinklers water valve if the system is enabled (e=1 is the enable condition of the switch e) and neither rain nor freezing temperatures are detected.

The rain sensor outputs a r=1 for rain, 0 otherwise; and the frost sensor outputs an f=1 for freezing temperatures, 0 otherwise. The irrigation system controller circuit outputs a single value i=1 that starts the irrigation system. Capture the desired system behavior using an equation, and then convert the equation to a circuit using AND, OR and NOT gates.

6. Under a base r system, the following equation is true:

[((34)_r) + ((24)_r)] x ((21)_r) = (1460)_r

Determine the base. You can make use of a calculator or a computer program to solve the roots.

7. Convert the following

a) 1792 (decimal) to Hexadecimal

b) 1792 (decimal) to Binary

c) 11100101 (binary) to Hexadecimal

d) A2DE (hexadecimal) to Decimal

e) 1100101 (binary) to Hexadecimal