# Digital Ckts & System - For ECE and IT Students

```Northern India Engineering College
Electronics &amp; Communication Engineering Department
ETEC-256 (Ms. Smriti Srivastava)
Assignment No. 1
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Solve ALL problems.
Only certain problems will be graded.
This Assignment is due in class one week from its date.
Problem 1. Perform the following system conversions
(i) (67.24)8 = ( ? )2
(ii) (11100.1001)2 = ( ? )16
(iii) (BC1.30)16 = ( ? )2
(iv) (10111.0111)2 = ( ? )8
(v) (67.67)8 = ( ? )10
(vi) (10110.0101)2 = ( ? )10
(vii) (155)10 = ( ? )2
(viii) (9714)10 = ( ? )8
(ix) (DEAD.BEE)16 = ( ? )8
(x) (DEAD.BEE)16 = ( ? )2
Problem 2 Simplifies the following Boolean algebraic expressions.
(a) ABC (ABC’ + AB’C + A’BC)
(b) XY (X’YZ’ + XY’Z’ + X’Y’Z’)
(c) XY + XYZ’ + XYZ’ + XYZ
Problem 3. Simplify the following Boolean algebraic expressions and draw a block
diagram of the circuit for each simplified expression using AND and OR gates.
(a) AB’C’ + A’B’C’ + A’BC’ + A’B’C
(b) A’BC + AB’C + A’BC + ABC’ + AB’C’ + A’BC’ + A’B’C’
(c) (A + B + C) (A + B’ + C’) (A + B + C’) (A + B’ + C)
Problem 4. Prepare the Truth Table for the following Boolean expressions:
(a) XYZ + X’Y’Z’
(b) (A + B) ( A + C) ( A’ + B’)
(c) AB + AC
Problem 5. Write the Boolean expression (in Sum of Products form) for the logic circuit
that will have a 1 output when X = 0, Y = 0, Z = 1 and X = 1, Y = 1, Z = 0, and a zero (0)
output for all other input states. Draw the logic diagram for this circuit.
Problem 6. Draw a logic diagram of your own provided that it has at least three inputs
and three gates (NOTs are not counted). Write the Boolean expression (function) and
generate the truth table for this circuit.
Problem 7. What is meant by Duality Theorem?
Problem 8. Prove that x + x = x?
Problem 9. Define Associative Law and Distributive law?
Problem 10. a. Express the Complement of the Following function in sum of Minterms
and product of Maxterms
F(A,B,C,D) = B’D+A’D + BD
b. Express the Complement of the following function in sum of Minterms
F (A, B, C, D) = Σ (0, 2, 6, 11, 13, 14)
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