Let's solve each question step by step: --- ### i. Convert 505₁₀ to binary using successive division. **Step-by-step:** - Divide the number by 2, write down the remainder, and repeat with the quotient until the quotient is 0. | Division | Quotient | Remainder | |---------------|----------|-----------| | 505 ÷ 2 | 252 | 1 | | 252 ÷ 2 | 126 | 0 | | 126 ÷ 2 | 63 | 0 | | 63 ÷ 2 | 31 | 1 | | 31 ÷ 2 | 15 | 1 | | 15 ÷ 2 | 7 | 1 | | 7 ÷ 2 | 3 | 1 | | 3 ÷ 2 | 1 | 1 | | 1 ÷ 2 | 0 | 1 | **Read the remainders from bottom to top:** - **505₁₀ = 111111001₂** --- ### ii. Write the BCD code for 505₁₀. **Step-by-step:** - BCD represents each decimal digit with its 4-bit binary equivalent. - 5 → 0101 - 0 → 0000 - 5 → 0101 **BCD for 505₁₀:** **0101 0000 0101** --- ### iii. ``` 1011 + 11 ``` First, write 11 in binary as 0011 to align digits: ``` 1011 + 0011 -------- ``` Add from right to left: - 1 + 1 = 0, carry 1 - 1 + 1 (carry) + 1 = 1, carry 1 - 0 + 0 + 1 (carry) = 1 - 1 + 0 = 1 So, the answer is: **1100** --- ### iv. What is the primary objective of clock signal in a sequential circuit? **Answer:** To synchronize the operations of sequential circuits, ensuring all components change state simultaneously based on the clock's timing. --- ### v. A flipflop is __________ triggered device while a latch is __________ triggered device. **Answer:** A flipflop is **edge** triggered device while a latch is **level** triggered device. --- ### vi. Arduino reads 0-1023 on the analog input pins. What is its ADC resolution? - 0 to 1023 is 1024 levels. - Resolution is log₂(1024) = 10 bits. **Answer:** **10 bits** --- ### vii. How can you avoid aliasing error during sampling when converting an analog signal? **Answer:** By using an anti-aliasing filter to remove frequency components above half the sampling rate (Nyquist frequency) **before** sampling. --- ### viii. What is the difference between an absolute encoder and an incremental encoder? **Answer:** - **Absolute encoder**: Provides a unique position value for each shaft position. - **Incremental encoder**: Only provides change in position (counts pulses) from a reference point. --- ### ix. Describe the working principle of a permanent magnet DC Motor. **Answer:** When current flows through the armature winding, it generates a magnetic field that interacts with the field from the permanent magnets, producing a torque that rotates the armature. --- ### x. What is a commutator and what is its main job? **Answer:** A **commutator** is a rotary switch in a DC motor or generator that reverses the direction of current in the armature windings, ensuring unidirectional torque. --- ## **Summary Table** | # | Answer | |-----|----------------------------------------------------------------------------------------------| | i | 505₁₀ = 111111001₂ | | ii | 505₁₀ in BCD: 0101 0000 0101 | | iii | 1011 + 11 = 1100 | | iv | Synchronize operations in sequential circuits | | v | Flipflop: edge-triggered, Latch: level-triggered | | vi | 10 bits | | vii | Use anti-aliasing filter before sampling | | viii| Absolute: unique position, Incremental: change in position | | ix | Interaction of armature current and permanent magnet field produces torque | | x | Commutator: reverses current direction, ensures unidirectional torque |

Certainly! Here's a detailed step-by-step explanation for each question along with the final answers: --- ### i. Convert 505₁₀ to binary using successive division. **Explanation:** To convert a decimal number to binary, repeatedly divide the number by 2, recording the remainder each time. Continue until the quotient becomes zero. The binary equivalent is obtained by reading the remainders from bottom to top. **Steps:** - 505 ÷ 2 = 252, remainder 1 - 252 ÷ 2 = 126, remainder 0 - 126 ÷ 2 = 63, remainder 0 - 63 ÷ 2 = 31, remainder 1 - 31 ÷ 2 = 15, remainder 1 - 15 ÷ 2 = 7, remainder 1 - 7 ÷ 2 = 3, remainder 1 - 3 ÷ 2 = 1, remainder 1 - 1 ÷ 2 = 0, remainder 1 Reading remainders from bottom to top: **111111001₂** **Final Answer:** **505₁₀ = 111111001₂** --- ### ii. Write the BCD code for 505₁₀. **Explanation:** BCD (Binary-Coded Decimal) encodes each decimal digit separately in 4 bits. - 5 in binary: 0101 - 0 in binary: 0000 For 505: - '5' → 0101 - '0' → 0000 - '5' → 0101 **Final Answer:** **BCD for 505 = 0101 0000 0101** --- ### iii. Add 1011₂ and 11₂. **Explanation:** Align the numbers by their least significant bits: - 1011₂ - 0011₂ (since 11₂ = 3 in decimal, padded to 4 bits) Perform binary addition: - 1 + 1 = 0, carry 1 - 1 + 1 + carry 1 = 1, carry 1 - 0 + 0 + carry 1 = 1, carry 0 - 1 + 0 = 1 Result: **1100₂** **Final Answer:** **1011 + 11 = 1100** --- ### iv. What is the primary objective of the clock signal in a sequential circuit? **Explanation:** The clock provides a timing reference that synchronizes the operation of sequential logic elements (like flip-flops). It ensures that state changes occur at specific times, preventing race conditions, and maintaining predictable circuit operation. **Final Answer:** **To synchronize the operations of sequential circuits by providing a timing reference.** --- ### v. A flip-flop is __________ triggered device while a latch is __________ triggered device. **Explanation:** - **Flip-flops** are **edge-triggered**, meaning they change state only at the rising or falling edge of the clock signal. - **Latches** are **level-triggered**, meaning they change state whenever the enable (or clock) signal is at a particular level (high or low). **Final Answer:** **A flip-flop is *edge*-triggered device while a latch is *level*-triggered device.** --- ### vi. Arduino reads 0-1023 on the analog input pins. What is its ADC resolution? **Explanation:** The ADC (Analog-to-Digital Converter) converts an analog voltage into a digital number between 0 and 1023. The number of discrete levels (2^n) corresponds to the resolution. - 1024 levels imply 10 bits because 2^10 = 1024. **Final Answer:** **10 bits** --- ### vii. How can you avoid aliasing error during sampling when converting an analog signal? **Explanation:** Aliasing occurs when higher frequency components in the signal are misrepresented as lower frequencies during sampling. To prevent this, apply an **anti-aliasing filter** (a low-pass filter) before sampling, which removes frequency components above half the sampling rate (Nyquist frequency). This ensures accurate representation of the signal. **Final Answer:** **Use an anti-aliasing filter to eliminate frequencies above half the sampling rate before sampling.** --- ### viii. What is the difference between an absolute encoder and an incremental encoder? **Explanation:** - **Absolute encoder:** Provides a unique position value for each shaft position, useful for knowing the exact position after power-up without needing to move to a reference point. - **Incremental encoder:** Provides pulses proportional to the change in position, which can be counted to determine movement but requires a reference point to know the absolute position. **Final Answer:** **Absolute encoder gives a unique position; incremental encoder provides relative movement (change in position).** --- ### ix. Describe the working principle of a permanent magnet DC motor. **Explanation:** When current flows through the armature winding of a PMDC motor, it creates a magnetic field. This interacts with the magnetic field of the permanent magnets, producing a force (Lorentz force) that causes the armature to rotate. The commutator switches the current in the windings to maintain continuous torque in one direction. **Final Answer:** **The magnetic interaction between the current-carrying armature and the permanent magnets produces torque, causing rotation.** --- ### x. What is a commutator and what is its main job? **Explanation:** A **commutator** is a rotary switch connected to the armature windings of a DC motor. Its main job is to reverse the direction of current in the windings each half turn, ensuring the torque produced by the motor remains in the same direction and the motor continues to rotate smoothly. **Final Answer:** **A commutator reverses the current direction in the armature windings, enabling unidirectional torque and continuous rotation.** --- If you need further clarification on any point, feel free to ask!