If a, b, c and d are inputs to a gate and x is its output, then, as per the following time graph, th

Q: How do I know where one time interval ends and another begins?

Look for the vertical edges where any signal transitions from low to high or high to low. Each transition marks the boundary of a new time interval.

Q: Why is the output $x$ high for almost the entire graph?

Because it's an OR gate! An OR gate outputs 1 if *any* of its inputs is 1. In this specific sequence, after the first interval, there is always at least one input that is high.

Q: What would the graph look like if it were an AND gate?

For an AND gate, the output $x$ would be 1 *only* in the very last interval where all inputs ($a, b, c, d$) are simultaneously high. For all other intervals, $x$ would be 0.

Q: Can a timing diagram represent a universal gate like NAND or NOR?

Absolutely. If it were a NOR gate, the output $x$ would be exactly inverted—it would be 1 only in the first interval and 0 everywhere else.

Q: Does the width of the pulses matter in identifying the gate?

No, the physical width (duration) of the pulses doesn't change the logic. What matters is the simultaneous state (high or low) of the inputs and the corresponding output at any given instant.

Question

If a, b, c and d are inputs to a gate and x is its output, then, as per the following time graph, the gate is

Options:

(A) NOT

(B) AND

(C) OR

(D) NAND

Sigma Percentile · Accepted Answer

### The Language of Timing Diagrams

Imagine you are looking at a musical score, but instead of notes, you have digital signals. A timing diagram is exactly that—a visual representation of how logic levels change over time. In this problem, we are given four input signals ($a, b, c, d$) and one output signal ($x$).

Our goal is to decode this visual symphony and figure out which logic gate is conducting it. To do this, we don't need to look at the whole graph at once. Instead, we slice it into vertical time intervals, just like reading a book frame by frame.

### Slicing Time into Intervals

Let's focus on the very first time interval, starting from $t = 0$. If you look at the graph, all four input signals—$a, b, c$, and $d$—are resting at their bottom level. In digital logic, this bottom level represents a logic **0**.

Now, look at the output signal $x$ during this exact same interval. It is also resting at the bottom. So, our first crucial observation is: when all inputs are **0**, the output is **0**.

### The Truth Table Reveal

As we move to the second time interval, something changes. The input $d$ jumps to its upper level, representing a logic **1**, while $a, b$, and $c$ remain at **0**. Instantly, the output $x$ also jumps to **1**.

If you continue scanning the rest of the timing diagram, you will notice a consistent pattern. Whenever at least one of the inputs is high (**1**), the output $x$ remains high (**1**). The output is only low (**0**) in that very first interval where every single input was low.

This behavior is the defining signature of an **OR gate**. An OR gate performs logical addition, meaning it outputs a true signal if any of its inputs are true. Therefore, the mystery gate is an OR gate!

Animated Solution for Physics - Semiconductors: If a, b, c and d are inputs to a gate and x is its output, then, as per the following time graph, the gate is

Select Answer:

Visualized Solution

Analyzing the Timing Diagram

First Time Interval

Subsequent Time Intervals

Identifying the Logic Gate

Conclusion

The Sigma Insight: Logic Gates

The Language of Timing Diagrams

Slicing Time into Intervals

The Truth Table Reveal

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