Gray code, with its unique property of single-bit changes between successive values, is widely used in applications such as rotary encoders and analog-to-digital converters. Its advantage lies in minimizing errors during transitions, making it robust for error detection and correction in telecommunications and electronic systems. Applying Gray code in position coding ensures smooth transitions in mechanical systems, and its use in optical encoders reduces reading errors caused by reflections. Additionally, in Binary Coded Decimal (BCD), Gray code simplifies the conversion between binary and decimal, making it useful in various fields. 1- Discuss the relationship between the angular resolution and the number of bits. Compute the resolution of 4-bits gray coded disk. 2- What would be the number of bits to provide a resolution of pi/512. 3- Write the truth table of the gray code with 4 bits. 4- Deduce the truth table of the gray code decoder (Gray bits as inputs and ordinary binary code as outputs). 5- Deduce the logic functions: b0(g3, g2,g1,g0), b1(g3, g2,g1,g0), b2(g3, g2,g1,g0), b3(g3, g2,g1,g0). 6- Using K-map, simplify the functions b0, , b3. 7- Realize the gray code decoder in EWB.

The display 7-segments is one of the oldest way to show messages, numbers or alphabetical characters. In order to display the numbers 0 to 9 on the 7-segments, a special encoding is necessary. The relationships between the LEDs of the display and the decimal njmbers explained in BCD format have to be revealed. Considering bits b0, b1, b2 and b3 as inputs to the encoder and LEDs (A, , G) are its outputs, answer the following questions: 1- Write the Truth Table of the encoder. 2- Conclude the logic functions A, B, , G. 3- Use the K-map to simplify the previous functions. 4- Implement the schematic in Electronic Work Bench

3- Project Implementation In practice, the output of the gray decoder has to be displayed in order to monitor the angular position and probably to do more complex computations related to the measured angle. The figure below shows the realization of such a monitor in a simple case with only one digit. Explain the realization of the system and the extend of the system to more general case with higher resolution and higher number of 7-segments

Deliverables By the end of the 4 sessions, all students have to submit individual reports thoroughly explained and illustrated to show the level of understanding. Schematic illustrations should be produced as screen shots of EWB software. Students have to provide three files surname_name_1.EWB and surname_name_2.EWB. surname_name_1.EWB Gray decoder schematic surname_name_2.EWB 7-segments schematic Four google classroom have been created and assigned to the groups 1, 2, 3 and 4. Every student has to access/check his classroom via the link sent by an email. The detailed report and the companion EWB files have to be uploaded to the google classroom by Sunday 24/12/2023 before midnight* . Good luck. Dr. Hasan