Provide detailed answers to the following:
1. Perform the following conversions:
a. 456.14 in Octal to Decimal
b. 1000.7 in Decimal to Hexadecimal
c. A5B.0C.in Hexadecimal to Octal
d. 11011.011 in Binary to Octal
2. Simplify the following:
a. xyz + x’y + xyz’
b. ABC + A’B + ABC’
c. (x + y)’ (x’ + y’)
3. List the truth table of the following functions. Also draw the logic diagram (gate implementation of the following functions)
a. F = xy + xy’ + y’z
b. Y = (A + B) (C’ + D)
4. Write the canonical sum of products and canonical product of sums for the following functions:
a. F = ΣX,Y,Z(0,3)
b. F = ΠA,B,C(1,2,4)
5. Write Verilog code to describe the following functions:
a. f1 = x1x3’ + x2x3’ + x3’x4’ + x1x2 +x1x4’
b. f2 = (x1 + x3’) . (x1 + x2 + x4’) . (x2 + x3’ + x4’)
6. A given system has 3 sensors that can produce an output of 0 or 1. The system operates properly when exactly one of the sensors has its output equal to 1. An alarm must be raised when two or more sensors have the output of 1. Design the simplest circuit that can be used to raise the alarm. Use K-MAP for the simplest circuit.
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