Question

Draw the timing diagram for four signals A3, A2, A1, and Ao, where A3 is the most significant bit, in binary code sequence, showing all possible output combinations.

Draw the timing diagram for four signals A3, A2, A1, and Ao, where A3 is the most significant bit, in Gray code sequence, showing all possible output combinations. Align it to your answer to part (a).

Answer 1

(a) In binary sequence:

A3: 0 0 1 1 0 0 1 1

A2: 0 0 0 0 1 1 1 1

A1: 0 1 0 1 0 1 0 1

A0: 0 1 1 0 0 1 1 0

(b) In Gray code sequence, aligned with (a):

A3: 0 0 1 1 1 0 0 1

A2: 0 1 1 0 0 0 1 1

A1: 0 0 0 1 1 1 0 1

A0: 0 0 1 0 0 1 1 0

The diagram can be seen on the attachment.

Step-by-step explanation:

In binary sequence, each b.i.t changes on every count, resulting in transitions across all possible combinations from 0000 to 1111. A3 changes at half the frequency of A2, A1, and A0. In Gray code, only one b.i.t changes at a time between successive values, preventing more than one b.i.t from changing simultaneously to minimize errors in digital systems. The Gray code sequence, aligned with the binary sequence, showcases how the transition between values occurs more orderly compared to the binary sequence, where multiple bits change simultaneously.

Correct Answers:

• (a) Binary sequence: A3: 00110011, A2: 00001111, A1: 01010101, A0: 01100110
• (b) Gray code sequence: A3: 00111001, A2: 01100011, A1: 00011101, A0: 00100110