State Diagram for a Sequence Detector - Mathematics Assignment Help

Assignment Task

Question 1
a) Give the state diagram for a ‘sequence detector’ whose output is 1 only if there is the sequence 1011 (first 1, second 0, third 1, fourth 1) at the input.

b) Perform the following subtraction using the 9s complement method. Explain how this method reduces subtraction into addition.

Question 2
a) Use truth tables to prove that
b) Given the Boolean function
use a Karnaugh map to derive a simpler equivalent expression as:
• sum-of –products 
• product-of-sums
X × X = 0
X + X ×Y = X + Y
ABCD ABCD ABCD ABCD ABCD ABCD ABCD

Question 3
a) Write the Boolean algebra expressions for the truth table
X Y Z Output
0 0 0 1
0 0 1 1
0 1 0 1
1 0 0 1
1 1 0 0
1 0 1 1
0 1 1 0
1 1 1 0

i) give your results in ‘sum-of-products’ form and draw the corresponding `AND-to-OR’ gate network
ii) give your results in ‘product-of-sums’ form and draw the corresponding `OR-to-AND’ gate network

b)Discuss the analogy between set theory and Boolean algebra. For the various operations in set theory, explain what are the corresponding operations in Boolean algebra.

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