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.

*Silly hint - you wear a pair (bi) of flip-flops.

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Just think - if it counts decades a decade is ten years or in this case just the number ten. So, for every decade it pulses once.

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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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Inserting a flip-flop into a circuit will divide the input signal (clock) by 2. Therefore to divide a frequency by 16 you simply need 4 flip-flops (in series).

Formula for solving this example:

\begin{align} 2^x &= 16\\ \ln{2^x} &= \ln{(16)}\\ x \times \ln{2} &= \ln{(16)}\\ x&=\frac{\ln{(16)}}{\ln{(2)}}\\ x&=4\\ \end{align}

Generalized formula for this situation:

\begin{align} 2^x &= y\\ \ln{(2^x)} &= \ln{(y)}\\ x*ln(2) &= \ln{(y)}\\ x &= \frac{\ln{(y)}}{\ln{(2)}}\\ \end{align}

Where \(y\) is the number to divide by and \(x\) is the number of flip-flops you will need.

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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

*astable: (electronics) Capable of oscillating between two states. An astable multivibrator is also called a free-running multivibrator (ARRL Handbook 1999 7-14)

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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.

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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This question is tricky. At first glance it seems to be asking about NOR gates, and the previous explanation cited that description. However, note the word “exclusive.” That means an XNOR gate, which is defined as:

A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results.

The wrong answers are:

• It produces logic "0" at its output only if all inputs are logic "0"

This is false because it produces logic 0 when only one input is 1.

• It produces logic "1" at its output only if all inputs are logic "1"

This is false, because it produces logic 1 when both inputs are 1 AND when both inputs are 0.

• It produces logic "1" at its output if any single input is logic "1"

This is false because it is the opposite of what it does. This answer descibes an XNOR gate.

The correct answer is:

• It produces logic "0" at its output if any single input is logic "1"

For more information:

https://en.wikipedia.org/wiki/XNOR_gate

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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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"Logic" refers to a finite number of states (usually but not always 2) that the circuit can have at each of its inputs and outputs. Logic can either be positive, in which case 0 is false and 1 is true, or it can be negative, in which case 1 is false and 0 is true. The former is how most people think of Boolean logic -- 0 is false, 1 is true. The latter is possible depending on the design of the circuit.

Here, "positive" refers to the voltage state at logic high, in other words when a 1 is represented. A high voltage represents a 1, low voltage a 0.

*Silly Hint - Think "Highly Positive". "High-ly (answer) Positive (question).

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