Digital Circuits: Decoders and Multiplexers

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Questions and Answers

What is the purpose of enable inputs in decoders?

To disable all outputs when not required. (correct)

To convert binary numbers to decimal.

To improve the speed of decoding.

To increase the size of the decoder.

How many 4-to-16-line decoders are needed to create a 6-to-64-line decoder?

Two

Four (correct)

Three

One

In a combination of two 2-to-4-line decoders to construct a 3-to-8-line decoder, which bit of the input controls the enable input of one decoder?

A2 (correct)

When A2 is equal to 0, which decoder is enabled and what are its output designations?

Upper decoder; D0 through D3 Signup and view all the answers

What happens when the enable input E of a decoder is set to 0?

All outputs are set to low level. Signup and view all the answers

What is the significance of using multiple decoders with the enable inputs in digital circuits?

To allow larger inputs while maintaining functionality. Signup and view all the answers

In a 3-to-8-line decoder arrangement using enable inputs, what role does the inverter play?

It controls the enable input of one of the decoders. Signup and view all the answers

Which of the following describes the outputs for the lower decoder when A2 is 1?

Outputs are dependent on A1 and A0. Signup and view all the answers

What output Y corresponds to the selection inputs S1 and S0 being equal to 00?

I0 Signup and view all the answers

Which statement is true regarding the function table of a 4-to-1 multiplexer?

Each combination of S1 and S0 results in a different input being selected. Signup and view all the answers

In the operation of the multiplexer, what is the role of the selection inputs S1 and S0?

To select one specific input to pass to the output. Signup and view all the answers

How many data inputs does a 4-to-1 multiplexer have?

4 Signup and view all the answers

What is another term for a multiplexer based on its function?

Data selector Signup and view all the answers

What kind of circuit do the AND gates and inverters in a multiplexer resemble?

Decoder circuit Signup and view all the answers

What is the general formula for the number of inputs in an n-to-2n multiplexer?

$2^n$ Signup and view all the answers

If S1 is 1 and S0 is 1, which input is selected for output Y?

I3 Signup and view all the answers

What role does the control unit serve in a digital computer?

It initiates sequences of microoperations. Signup and view all the answers

Which two methods are used to implement the control unit in digital systems?

Hardwired control and micro-programmed control. Signup and view all the answers

What determines the complexity of a digital system?

The number of sequences of microoperations. Signup and view all the answers

Which of the following is NOT a functional part of a digital computer?

Timing Unit Signup and view all the answers

What are the main components of the Central Processing Unit?

Control unit, arithmetic and logic unit, and registers. Signup and view all the answers

What is the maximum count of an n-bit binary counter?

$2^n - 1$ Signup and view all the answers

What must be true for a bit to be complemented in a binary counter?

All lower-order bits must be 1 Signup and view all the answers

Which flip-flops are typically employed in binary counter circuits?

T and JK flip-flops Signup and view all the answers

In a sequence of binary counts, how does the low-order bit change?

It changes with every count Signup and view all the answers

What condition leads to the complementing of the third-order bit during counting?

If the first two bits are equal to 1 Signup and view all the answers

What is the effect when both J and K inputs of a JK flip-flop are 1 during a clock transition?

The output is toggled Signup and view all the answers

Which statement is true about the sequence followed by an n-bit binary counter?

It follows a specific pattern for each bit Signup and view all the answers

What is the primary function of gates in an n-bit binary counter?

To manage the state transitions of the flip-flops Signup and view all the answers

What happens to the output when the Enable (E) signal is set to 0?

The outputs all become 0's. Signup and view all the answers

Under which condition will the four A inputs be routed to the outputs?

When E is 1 and S is 0. Signup and view all the answers

What function do multiplexers typically perform?

Data routing, parallel-to-serial conversion, and logic function generation. Signup and view all the answers

How can an n-variable logic function be generated using a multiplexer?

By using n-select inputs. Signup and view all the answers

What is the state of outputs when the Select (S) line is set to 1 and E is enabled?

Outputs reflect the values of the B inputs. Signup and view all the answers

What can be inferred about the multiplexers in the described circuit?

They can function as universal logic modules. Signup and view all the answers

In a multiplexer, what enables the paths from inputs A and B to their respective outputs?

Both the Enable (E) and Select (S) signals. Signup and view all the answers

What is the impact of the Select (S) signal in operation?

It controls whether A or B inputs are sent to the outputs. Signup and view all the answers

What happens to the register when the clear control is activated?

The register is cleared to 0 regardless of other inputs. Signup and view all the answers

Under what condition is the data loaded into the flip-flops?

When the clear control is disabled and load input is 1. Signup and view all the answers

What role do counters with parallel load play in digital computers?

They act as registers capable of loading and incrementing values. Signup and view all the answers

What must be true for the increment input regarding the loading process?

It can be either 0 or 1 while loading occurs. Signup and view all the answers

What happens if the clear control is enabled while the load input is also high?

The register will ignore the load and be set to 0. Signup and view all the answers

How many bits does the example counter design presented utilize?

4 bits Signup and view all the answers

What input configuration can enable clearing the register?

Clearing occurs regardless of load or increment input states. Signup and view all the answers

Which control input must be set to 1 for the flip-flops to load data?

Load control Signup and view all the answers

Study Notes

Digital Components

Integrated circuits (ICs) are small semiconductor crystals (chips) containing electronic components for digital gates.
Gates are interconnected on a chip to form the required circuit.
IC chips are mounted in ceramic or plastic containers.
Connections are welded with gold wires to external pins.
Pin numbers vary from 14 to 100+ depending on the IC package size.
Data books or catalogs by vendors contain detailed descriptions and specifications of ICs.
Technology advancements have significantly increased IC gate counts.
Small-scale integration (SSI) has fewer gates (usually less than 10).
Medium-scale integration (MSI) has gates ranging from 10 to 200.
Large-scale integration (LSI) has between 200 and a few thousand gates.
Very-large-scale integration (VLSI) has thousands of gates.
Digital integrated circuits are also classified by the logic family type.

Decoders

Decoders convert binary codes into a maximum of 2ⁿ unique outputs.
3-to-8-line decoder has three input variables decoded into eight separate outputs.
Decoders often have one enable input (E), switching on and off the decoder.
When enabled (E = 1), a binary code in the input is output on the designated output.
When disabled (E = 0), all outputs are 0.

NAND Gate Decoder

Some decoders use NAND gates instead of AND gates.
NAND gate decoders have a complemented enable input (E).
The decoder is enabled when E = 0, disabled when E = 1.

Decoder Expansion

Decoders can be expanded using smaller decoders with enable inputs.
For example, a 6-to-64-line decoder can be constructed with four 4-to-16-line decoders.
They are connected in a way where input bits are shared between decoders.
Enable inputs are used for expanding multiple decoders for one circuit.

Encoders

Encoders perform the inverse function of a decoder.
They have 2ⁿ (or fewer) input lines and n output lines (converting an octal-to-binary code for example).

Multiplexers

Multiplexers (MUXs) select one of 2ⁿ input data lines and direct it to a single output line.
Multiplexers have a set of selection inputs determining which input goes to the output.
For example, a 4-to-l-line multiplexer has four data inputs and 2 selection inputs.

Registers

Registers are groups of flip-flops used to hold binary information (n-bit register has n flip-flops).
Additional logic gates control data transfer.
'Parallel load' loads all bits simultaneously with a clock pulse.

Shift Registers

A shift register is a cascade of flip-flops where output of one flip-flop feeds into the next.
Data movement occurs when shifted with clocked pulses.
Unidirectional shift registers can only shift in one direction.
Bidirectional shift registers can shift in both directions.
Parallel loading is possible, storing multiple bits simultaneously.

Binary Counters

Binary counters are registers that follow a sequence of states upon input pulses.
Usually used for counting events or generating timing signals.
Synchronous binary counters have a fixed and predictable counting sequence.
Often have a parallel load capability for pre-setting a starting value.

Memory Unit

Memory units store binary information in words.
Each word has several bits, and each word has a unique address.
Random access memory (RAM) allows data to be retrieved from any location instantly.
Read-only memory (ROM) has pre-programmed constant data.

Control Memory

Control memory stores microinstructions that control CPU microoperations.
Microinstructions control the sequence of microoperations for a given instruction.

Microprogrammed Control

An elegant and systematic method for controlling microoperations in a computer.
Uses stored microinstructions within a control memory, with a sequencer determining the next address in the sequence.
Allows for changes to a computer's instruction set without changing the hardware, by changing only the microprogram.
Enables flexible and efficient handling of a wider number of instructions.

Address Sequencing

The hardware within the control unit controls the address sequencing of the control memory.
It sequences microinstructions in a routine and enables branching between routines.
This is done by incrementing the control address register (CAR) for sequential operations or by loading a branch address in response to a branch instruction.

Conditional Branching

Decisions are made within the control unit based on status bits (carry, zero, sign, overflow).
The branch conditions determine whether or not a branch occurs.

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Description

This quiz explores essential concepts of digital circuits, focusing on decoders and multiplexers. It covers the functions of enable inputs, the relationship between different types of decoders, and the role of selection inputs in multiplexers. Test your understanding of these fundamental components in digital design.