Question

Prove that in 4B/5B mapped data with the NRZI encoding, a signal transition will occur at least every four bit times.

a. Proof by Contradiction
b. Proof by Induction
c. Direct Proof
d. Proof by Counterexample

Answer 1

In 4B/5B encoding used with NRZI, every 4-bit data is mapped to a 5-bit sequence with at least one '1', guaranteeing a signal transition in NRZI encoding at least every four bits.

Step-by-step explanation:

The student's question pertains to the proof that a signal transition will occur at least every four bit times in 4B/5B mapped data with Non-Return-to-Zero Inverted (NRZI) encoding. This can be clarified by a direct proof.

In 4B/5B encoding, every 4 bits of data is mapped into a 5-bit sequence. These 5-bit sequences are designed such that they always contain at least one '1'. Since NRZI encoding involves a change in the signal level whenever a '1' is encountered (and no change for a '0'), this ensures that a signal transition occurs at least once within each 5-bit sequence, which is more frequent than once every four bits.

Therefore, due to the inherent properties of 4B/5B encoding and NRZI signal transitions on '1's, a transition must happen at least every four bits. This direct proof confirms the statement without the need for contradictions, inductions, or counterexamples.