First Month Exam PDF - Digital Principles

First month exam Digital principles Dr.: Daoud True/False Questions 1. The binary number system is a weighted system with two digits. (True) 2. The octal number system consists of eight digits, 0 through 7. (True) 3. The 1’s complement of the binary number 1010 is 0101. (True) 4. The hexadecimal nu...

First month exam Digital principles Dr.: Daoud True/False Questions 1. The binary number system is a weighted system with two digits. (True) 2. The octal number system consists of eight digits, 0 through 7. (True) 3. The 1’s complement of the binary number 1010 is 0101. (True) 4. The hexadecimal number system has 16 characters, six of which are alphabetic. (True) 5. A decimal number can be converted to binary using repeated division by 2. (True) Multiple-Choice Questions 11. What is the decimal equivalent of the binary number 1101? a) 11 b) 12 c) 13 d) 14 Answer: (c) 13 12. Convert the decimal number 21 to binary. a) 10001 b) 10101 c) 11000 d) 11111 Answer: (b) 10101 13. The binary equivalent of hexadecimal 1F is: a) 1111 b) 10001 c) 11111 d) 11010 Answer: (c) 11111 15. The sum of the binary numbers 1101 + 0110 is : a) 1011 b) 1111 c) 10011 d) 11011 Answer: (c) 10011 17. Which number system has a base of 8? a) Decimal b) Octal c) Hexadecimal d) Binary Answer: (b) Octal 18. What is the hexadecimal equivalent of decimal 255? a) A9 b) FF c) 100 d) 10A Answer: (b) FF Conversion Questions. 21-Convert 57 decimal to binary. Answer: 111001 23. Convert 3A hexadecimal to decimal. Answer: 58 25. Convert 110011 binary to hexadecimal. Answer: 33 26. Convert 765 octal to binary. Answer: 111110101 29. Convert 101011 binary to octal. Answer: 53 30. Convert A9 hexadecimal to binary. Answer: 10101001 Binary Arithmetic Questions 31. Perform 1010 + 1101 in binary. Answer: 10111 32. Perform 1001 - 0111 in binary. Answer: 0010 33. Multiply 110 * 101 in binary. Answer: 100110 39. Add 00100001 + 10111100 in binary. Answer: 11011101 40. Subtract 01110111 - 00110010 in binary. Answer: 01000101 True/False Questions 2. An AND gate outputs 1 if at least one input is 1. (False) 3. The NOR gate produces a high output only when all inputs are low. (True) 5. The XOR gate produces an output of 1 when both inputs are 1. (False) 6. The output of an AND gate is always the same as the input when there is only one input. (True) 9. The logic gates in a circuit are defined using Boolean expressions. (True) Multiple-Choice Questions 12. Which gate produces an output of 1 when both inputs are 0? a) AND b) OR c) NOR d) XOR Answer: (c) NOR 14. What is the output of a NAND gate when both inputs are 1? a) 0 b) 1 c) Undefined d) None of the above Answer: (a) 0 15- A logic gate that can implement any Boolean function is: a) XOR b) AND c) NAND d) OR Answer: (c) NAND 19. Which gate produces a high output only when all inputs are high? a) OR b) AND c) NOR d) XOR Answer: (b) AND 21. Construct a truth table for an AND gate with three inputs. Answer: The output is 1 only when all three inputs are 1. 22. Construct a truth table for an OR gate with three inputs. Answer: The output is 1 when at least one input is 1. 23. If the inputs to an XOR gate are A = 1 and B = 1, what is the output? Answer: 0 24. What is the output of a NAND gate with inputs A = 0, B = 1? Answer: 1 26. Which logic gate has the same truth table as a NOR gate followed by an inverter? Answer: OR gate 28. The Boolean expression A + AB simplifies to: Answer: A 30. If an AND gate has three inputs and one of them is 0, what is the output? Answer: 0 32. If an OR gate produces a 0 output when both inputs are 0, is the gate functioning correctly? Answer: Yes Circuit Analysis and Troubleshooting 33. A logic circuit has three inputs and produces an output of 1 when an odd number of inputs are 1. What type of gate is used? Answer: XOR gate 35. A faulty NAND gate is always outputting 0. What could be the issue? Answer: One or both inputs are stuck at 1.. 37. If an inverter (NOT gate) has an input of 1, what is the output? Answer: 0 38. A circuit needs an output of 1 when both inputs are different. What gate should be used? Answer: XOR gate 42. Apply DeMorgan’s theorem to (A + B + C)'. Answer: A'B'C' 43. Construct a logic circuit for the expression AB + A'B. Answer: XOR gate 44. Simplify the expression AB + A(B + C). Answer: AB + AC 46. Convert a NAND gate to an AND gate using an additional gate. Answer: Use an inverter (NOT gate) after the NAND gate. 48. In a truth table for an XOR gate, what is the output when both inputs are 0? Answer: 0. True/False Questions 1. Boolean algebra is used to analyze and simplify digital logic circuits. (True) 3. The distributive law states that A(B + C) = AB + AC. (True) 4. DeMorgan’s theorem states that (AB)’ = A’ + B’. (True) Multiple-Choice Questions 11. The commutative law states that: a) A + B = AB b) A + B = B + A c) A(B + C) = AB + AC d) A(B + C) = AB Answer: (b) A + B = B + A 12. What is the result of applying DeMorgan’s theorem to (A + B)’? a) A’B’ b) A + B c) A’ + B’ d) AB Answer: (a) A’B’ 14. Which Boolean algebra law states A(A + B) = A? a) Identity law b) Absorption law c) Associative law d) Distributive law Answer: (b) Absorption law 21. Simplify A + AB. Answer: A 22. Apply DeMorgan’s theorem to (AB)’ Answer: A’ + B’ 25. Convert the Boolean equation A(B + C) into its expanded form. Answer: AB + AC 26. Use a Karnaugh map to simplify A B C + ABC + ABC + ABC. Answer: A + BC 31. Construct a truth table for the function X = A + B. Answer: X is 1 if either A or B is 1. 32. Construct a truth table for the function X = AB. Answer: X is 1 if both A and B are 1. 34. What is the binary output of a NAND gate with inputs A = 1, B = 1? Answer: 0 35. What is the binary output of a NOR gate with inputs A = 0, B = 0? Answer: 1 36. Identify the Boolean function of a 3-input AND gate. Answer: Output is 1 only when all inputs are 1. 37. Identify the Boolean function of a 3-input OR gate. Answer: Output is 1 when at least one input is 1. 38. If A = 1, B = 0, and C = 1, find the output of X = AB + C. Answer: 1 39. What is the function of a NOT gate? Answer: It inverts the input. 47. Convert the truth table {A=0, B=1, X=1} into a Boolean equation. Answer: A’B Good luck to everyone