For the timing diagram below, define the sequence of values y holds in each of the timing segments 0-7 (from left to right) for y = a OR NOT b.

Question

BlackTom AI · Accepted Answer

We are given the timing diagram for signals a and b across 8 segments (0 through 7) and the output y is defined as y = a OR NOT b. To evaluate each candidate sequence, we must read the values of a and b in every segment from the diagram and compute NOT b, then perform the OR operation with a for that segment.

Option 1: y = 1 1 1 0 1 1 0 1
- Step-by-step check: For each segment, compare the computed y with this sequence.
- If in any segment a = 0 and b = 1 (so NOT b = 0), then y would be 0, contradicting a 1 in this option. Conversely, if a = 1 or NOT b = 1 in a segment, y would be 1, matching a 1 in this option. Evaluate each segment accordingly and see if all 8 positions line up. If any segment mismatches, this option is incorrect.

Option 2: y = 0 1 1 1 1 1 1 0
- Step-by-step check: This sequence asserts zeros at segments 0 and 7, and ones elsewhere. For segment 0, the only way y = 0 is if a = 0 and NOT b = 0 (i.e., a = 0 and b = 1). Verify whether the diagram shows a = 0 and b = 1 in segment 0. If not, this option is invalid. Do the same cross-segment comparison for segments 1 through 6 where y = 1 in this option; each segment must have a = 1 or NOT b = 1.

Option 3: y = 0 0 1 0 0 1 0 0
- Step-by-step check: This sequence has many zeros. For segments where y = 0, both a must be 0 and NOT b must be 0 (i.e., a = 0 and b = 1). Identify which segments could satisfy this (0s at 0,1,3,4,6,7) and confirm whether the diagram indeed shows a = 0 and b = 1 in those segments. For segments with y = 1 (segments 2 and 5), ensure that either a = 1 or NOT b = 1 holds in those segments. If any of these conditions fail, the option is invalid.

Option 4: y = 1 0 1 1 0 1 1 1
- Step-by-step check: Here zeros appear at segments 1 and 4 only. For segment 1 to yield y = 0, both a = 0 and NOT b = 0 must hold (a = 0 and b = 1). Check the diagram’s values in segment 1. For segment 4 similarly, require a = 0 and b = 1. If the diagram shows either a = 1 or b = 0 (making NOT b = 1) in any of those segments, the option would be invalid. For the segments where y = 1 (0,2,3,5,6,7), confirm that at least one of a = 1 or NOT b = 1 is true according to the timing diagram.

General observations to distinguish options:
- The OR with NOT b means y will be 1 in any segment where either a is 1, or b is 0 (since NOT b would be 1 when b = 0).
- Thus, segments where b is asserted high (b = 1) and a is low (a = 0) should produce y = 0 only if also a = 0; in all other cases y becomes 1 due to a = 1 or NOT b = 1.
- A lot of these options differ mainly in the first and last few segments, where the combination of a and b can flip y depending on whether NOT b is active.

Cross-check strategy you can apply quickly on the diagram:
- For each segment, write the pair (a, b). Compute NOT b, then compute y = a OR NOT b. This gives the correct 8-bit sequence. Then compare with each option.
- If you find a single segment where the option’s bit disagrees with the computed bit, discard that option.

Note: Without reprinting the exact a/b values per segment from the diagram in text, identifying which option is correct relies on performing this per-segment computation directly from the timing diagram. If you recount the values of a and b for segments 0–7 from the image and run the above logic, you will determine which of the listed sequences matches y = a OR NOT b for all 8 segments.

For the timing diagram below, define the sequence of values y holds in each of the timing segments 0-7 (from left to right) for y = a OR NOT b.

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