A clock is a device that is periodically switching states, and so is not stable because its output does not remain in a particular state. The outputs of AND and OR gates immediately reflect the inputs of their corresponding circuits, and so are not considered stable circuits. A flip-flop can retain its output state(s) after one or more of its inputs have changed, and so is stable in either of its binary states, making it a bistable circuit.

To help you remember: a flip-flop is stable in two (bi-) different states.

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In this case, it is assumed that the T input of the T flip-flop is asserted, since de-asserting the T input will prevent the output level from changing. The output level of a T flip-flop changes state with the next clock input. So, the output level changes every time the clock, or trigger, pulses. Therefore, if the trigger pulses twice, the output level changes twice.

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Answer An XOR gate is wrong, because an XOR gate merely performs an exclusive OR operation on two or more inputs.

Answer OR gate is wrong, because an OR gate merely performs a logical OR operation on two or more inputs.

Answer A multiplexer is wrong, because a multiplexer selects one of several possible inputs according to some selector signals.

Answer A flip-flop is correct. Division by two of a pulse train is accomplished by attaching the pulse train to the flip flop's clock, and feeding back the logical negation of the flip flop output to its input.

Suppose the flip flop output starts out at logical 1. On the rising edge of the next pulse presented at the flip flop's clock input, the flip flop output toggles to logical 0. It remains at this value as the pulse falls back to 0. On the rising edge of the following pulse the flip flop output flips back to logical 1. Because the flip flop's output changes half as frequently as its clock input changes, we say that it divides the input frequency by 2.

See a tutorial on frequency division for illustrations.

Hint: You have 2 flip-flops.

Another silly hint: Thru-hikers sometimes Flip-Flop dividing the trail in two.

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A Flip-flop takes in a signal. The signal is output as either Q or Not Q. By feeding the Not Q back in, the flip-flop divides the frequency by 2. To divide the frequency by 4 you need 2 flip-flops.

Another way to think of this is that you need to be able to count four numbers in binary to divide by 4:

• 0 = b00
• 1 = b01
• 2 = b10
• 3 = b11

Each flip-flop stores one bit, and you needed two digits (bits) to do that thus you need two flip-flops.

Hint: You have 2 flip-flop shoes.

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An astable multivibrator consists of two amplifying stages connected in a positive feedback loop by two capacitive-resistive coupling networks. It continually switches from one state to the other.

Multivibrator circuits are frequently used in two-state devices. The question asks about a circuit that continuously alternates without an external clock.

We can immediately eliminate both flip-flop answers because flip-flops change state on input, and the question specifies no external clock. Flip-flops are bistable multivibrators.

We can eliminate "monostable multivibrator" because these circuits are stable in one state: they change state on input and then return to their stable state.

It's enough to simply examine the words used. The question asks for a circuit that continuously changes. This means that it has zero stable states. "Astable" means "no stable", "monostable" means "single stable", and flip-flops are "bistable", or "two-stable."

Alt Hint: 'Ast' is able to alternate two states

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A Multivibrator is an electronic circuit used to implement a variety of simple two-state systems such as oscillators, timers and flip-flops. There are three types, astable, monostable and bistable.

A Monostable Multivibrator is an electronic circuit in which one of the states is stable, but the other state is unstable (transient). A trigger pulse causes the circuit to enter the unstable state. After entering the unstable state, the circuit will return to the stable state after a set time. Such a circuit is useful for creating a timing period of fixed duration in response to some external event. This circuit is also known as a one shot.

Hint: There are two large words that start with 'M' in the question. The correct answer is the only one that has a large word that starts with an 'M' (momentarily) in it.

Source: Wikipedia - Multivibrator

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The name of a NAND gate indicates it has the effective function of an AND gate followed by a NOT gate. The NOT gate output is the inverse of the input. The AND gate provides an output logic "1" only when both of the inputs are logic "1". So, adding the NOT gate creates the inverse behavior, and the output is logic "0" only when both of the inputs are logic "1".

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A logical OR is different from the way we commonly use the word "or" in English.

In English we use "or" as one or the other. In formal logic, that is called an "exclusive or" or XOR.

In logic OR is true if either or both are true.

Memory aid for this answer: "Or" = "any or all"

A silly HINT: Correct answer has the word, “or” as does the question.

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A truth table is a mathematical table used in logic to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their logical variables. In particular, truth tables can be used to tell whether a propositional expression is true for all legitimate input values, that is, logically valid.

In other words, a truth table is a table composed of rows and columns, which express the corresponding output to each of the possible combinations of inputs.

Source: Enderton, 2001

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Positive logic is where the "1" state is defined as having a MORE positive voltage than the "0" state.

Negative logic is where the "1" state is defined as having a MORE negative voltage than the "0" state.

"When a circuit requires logic 1 to operate, engineers may refer to this condition as positive logic. Thus, the more positive voltage causes the action to take place. On the other hand, if a circuit requires a logic 0 to cause action, this type circuit is referred to as negative logic. There is nothing negative or positive about these various circuits. The notation simply provides a shorthand that tells engineers and users whether a logic 1 or a logic 0 causes an action." The Digital I/O Handbook, Chapter 1 Logic Principles, Tom O'Hanlan and Jon Titus

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"When a circuit requires logic 1 to operate, engineers may refer to this condition as positive logic. Thus, the more positive voltage causes the action to take place. On the other hand, if a circuit requires a logic 0 to cause action, this type circuit is referred to as negative logic. There is nothing negative or positive about these various circuits. The notation simply provides a shorthand that tells engineers and users whether a logic 1 or a logic 0 causes an action." The Digital I/O Handbook, Chapter 1 Logic Principles, Tom O'Hanlan and Jon Titus

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The SR stands for Set/Reset so you can eliminate choices A and C. An SR flip-flop has no T input (but a T flip-flop does) so you can eliminate choice D. That leaves B.

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For this question you just have to know that the JK flip-flop is a variation on the RS flip-flop.

The R and S stand for Set and Reset inputs to a flip-flop; however, the J and K inputs are just named by random consecutive letters of the alphabet.

The above is true for the purpose of answering the question, but the another distinction between the RS and JK flip flop lies in the fact that the RS flip flop is an Asynchronous device that does not involve a clock signal and the JK flip flop is a Synchronous device that involves a clock signal to sample the state of the inputs only on the active clock level.

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The D flip-flop is widely used. It is also known as a "data" or "delay" flip-flop. Read more

A D flip flop changes its output whenever the clock goes from low (0) to high (1). Any changes to the input while the clock signal is unchanged or transitioning from high to low are not reflected in the D flip flop's output.

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