Binary Encoder-Decoder | Computer Systems

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Questions and Answers

What is the primary function of an encoder in the context of digital circuits?

  • To convert multiple input lines into a smaller number of output lines. (correct)
  • To amplify the signal strength of input lines.
  • To convert a smaller number of input lines into a larger number of output lines.
  • To regulate the voltage levels of input lines.

A combinational logic circuit has four input lines and two output lines. What type of encoder is this?

  • A 4-to-2 encoder (correct)
  • A 4-to-1 encoder
  • A 1-to-4 encoder
  • A 2-to-4 encoder

In digital logic, what does a priority encoder do that a simple binary encoder does not?

  • It decreases the number of output lines.
  • It increases the number of input lines.
  • It converts analog signals to digital.
  • It assigns a priority to each of the inputs. (correct)

If multiple inputs are active simultaneously, which type of encoder is required?

<p>A priority encoder. (B)</p>
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How many inputs does a binary encoder with n output lines have?

<p>2 to the power of n (C)</p>
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What is the key limitation of a standard binary encoder when multiple inputs are active?

<p>It can only have one active input at any time. (B)</p>
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In the context of a binary encoder, what does it mean for the input lines to be 'activated' for one possible combination of the output lines?

<p>The values of inputs uniquely determine the output. (C)</p>
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Which of the following scenarios would necessitate the use of a priority encoder over a standard binary encoder?

<p>Detecting which key was first pressed on a keyboard when multiple keys are pressed simultaneously. (B)</p>
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Which operation does an encoder perform in relation to a decoder?

<p>Opposite operation. (A)</p>
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What is the purpose of designing an interface using a binary encoder to encode 10 separate input switches?

<p>To convert the switch positions into a corresponding binary value. (B)</p>
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In a decimal-to-BCD encoder, what does 'BCD' stand for?

<p>Binary Coded Decimal (B)</p>
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When a decimal 3 is activated in the input of a Decimal to BCD encoder, what is its 4-bit BCD output?

<p>0011 (D)</p>
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Given a decimal-to-BCD encoder, determine the binary coded decimal (BCD) output for the decimal input '9'.

<p>1001 (A)</p>
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What is the purpose of using a decoder in the design of a binary half-adder?

<p>To convert binary inputs into a different format, which a combination of OR gates can use to compute sum and carry. (A)</p>
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Which binary operation does a 'half-adder' circuit perform?

<p>Performs the addition of two single-bit binary numbers. (D)</p>
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In a half-adder circuit, what does the Carry (C) output represent?

<p>The most significant bit of the addition result. (C)</p>
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In the context of a half-adder, what does the Sum (S) output represent?

<p>The least significant bit of the addition result. (A)</p>
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Construct a truth table for a half-adder. What are the outputs C (carry) and S (sum) when both inputs A1 and A0 are 1?

<p>C=1, S=0 (D)</p>
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For a half-adder with inputs A0 and A1, what are the logic equations for the carry (C) and sum (S) outputs?

<p>C = A0 * A1, S = A0 XOR A1 (B)</p>
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If we have 2-inputs A0 and A1, what will be the size of the decoder used to design the half-adder?

<p>2 x 4 (A)</p>
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Given a 2-to-4 decoder with inputs A0 and A1, which of the following outputs represents the term $A0 * A1$?

<p>$A0 * A1$ (B)</p>
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What will be the boolean expression if a decoder and gates are used?

<p>Simplified (B)</p>
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Which component is often used to convert BCD to a format suitable for driving a 7-segment display?

<p>Decoder (B)</p>
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What type of components can be used to implement boolean expressions?

<p>Decoders and gates. (D)</p>
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According to the truth table, what formula represents A0?

<p>D1 + D3 (C)</p>
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According to the Truth Table, what is the boolean formula to represent A1?

<p>D2 + D3 (D)</p>
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How does a decoder contribute to the implementation of Boolean expressions?

<p>By generating minterms that can be combined using gates. (D)</p>
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Examine a scenario where a keypad is designed with a binary encoder. How does the encoder facilitate the keypad's functionality?

<p>By translating each keypress into a unique binary code. (A)</p>
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In the context of binary encoders, what does the term '$2^n$' represent in relation to the number of input and output lines?

<p>The number of input lines, given 'n' output lines. (D)</p>
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Consider the binary encoder circuit diagram. What do the OR gates accomplish in the conversion process?

<p>They combine the signals from different input lines to generate the output code. (C)</p>
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How can a 2-to-4 decoder, in association with other logic gates, be utilized in creating a half-adder digital circuit?

<p>By generating the necessary minterms that logic gates combine. (D)</p>
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Given the equations that relate to the decimal-to-BCD encoder, what is the meaning of B = 4 + 5 + 6 + 7?

<p>B gets set to 1 if any digits of 4, 5, 6, or 7 are active. (A)</p>
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A BCD-to-7-segment display decoder is used. How does this facilitate the displaying of numbers?

<p>By transforming BCD input into a format comprehensible by the display. (D)</p>
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In a 2-to-4 decoder being used to implement a half-adder, how are the AND and XOR functions accomplished?

<p>AND and XOR operations get synthesized through the appropriate interconnections. (C)</p>
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In computer architecture, what is the role of encoders and decoders in memory addressing?

<p>To simplify memory access by reducing the number of address lines. (B)</p>
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Consider a decimal-to-BCD encoder used in a digital calculator. What is the purpose of this encoder within the calculator's architecture?

<p>Converting decimal inputs from the keypad into BCD for processing. (A)</p>
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If multiple inputs are activated, what circuit can be used?

<p>Priority Encoder (D)</p>
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Flashcards

What is an encoder?

A combinational logic circuit that converts multiple input lines into a smaller number of output lines.

What is a binary encoder?

This type converts 2^n inputs into an n-bit binary code.

What is a priority encoder?

This type assigns priority to the inputs.

What is a decoder?

An encoder performs the inverse operation of this.

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How are the input lines activated?

Input lines are activated for only one possible combination of output lines.

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What is a truth table for an encoder?

A table showing the relationship between inputs and outputs of an encoder.

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What is a limitation of binary encoders?

Only one input can be active at any time.

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What is a keypad encoder application?

Designs an interface to encode multiple separate input switches and output a binary value for each switch.

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What does a decimal-to-BCD encoder do?

Encodes 10 decimal inputs to produce a 4-bit BCD output.

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What is a half adder?

A basic digital circuit that performs binary addition of two single-bit binary numbers.

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What is Sum (S)?

Represent the least significant bit (LSB) of the addition in a half adder.

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What is Carry(C)

Represents the most significant bit (MSB) of the addition.

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What is the truth table for a half-adder?

A table that shows how A1 and A0 relate to Carry and Sum values.

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What is a 7-segment display?

A simple display component that can show decimal digits.

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Study Notes

  • CSIT 230 is a computer systems course at Montclair State University.
  • The instructor is Dr. Prince Waqas Khan.

Binary Encoder-Decoder

  • Encoders are combinational logic circuits.
  • Encoders convert multiple input lines into fewer output lines.
  • Each input is represented by a unique binary code.
  • There are different types of encoders, including Binary and Priority Encoders.
  • A Binary Encoder converts 2n inputs into an n-bit binary code; an example is a 4-to-2 encoder.
  • A Priority Encoder assigns priority to inputs and outputs the code of the highest-priority active input.
  • An encoder performs the inverse operation of a decoder.
  • Encoders encode binary information into a more compact binary form
  • A binary encoder converts 2n input lines into n output lines.
  • Input lines for Encoders are activated for only one possible combination of the output lines.
  • In a typical block diagram 4 inputs are converted to 2 outputs
  • Encoders take n inputs to create m=2n outputs.
  • In binary encoders, only one input can be active at any time.
  • If more than one input needs activation, a priority encoder is required.

Truth Table & Logic Expressions

  • For a binary encoder, given inputs D3, D2, D1, and D0, the outputs are A1 and A0.
  • If D0 is 1, then A1 and A0 are 0.
  • If D1 is 1, then A1 is 0 and A0 is 1.
  • If D2 is 1, then A1 is 1 and A0 is 0.
  • If D3 is 1, then A1 and A0 are 1.
  • The Logic equations for the encoder, and given the inputs D1 and D3, then A0 = D1 + D3
  • Given inputs D2 and D3, then A1 = D2 + D3
  • The circuit diagram shows OR gates combining D1+D3 to produce A0, and D2+D3 to produce A1.

Specific applications of Binary Encoders

  • Keypads have interfaces designed to encode separate input switches.
  • Keypads output a binary value corresponding to each input switch.
  • An example includes designing an interface to encode 10 separate input switches to output the binary value corresponding to each input switch

Decimal to BCD Encoder

  • Decimal to BCD Encoders' Truth Table contains decimal numbers 0 - 9 as input, and a BCD output
  • When an input is activated, encoder output is the 4-bit binary equivalent of the decimal number.
  • The equations for conversion are: A = 8+9, B = 4+5+6+7, C = 2+3+6+7, D = 1+3+5+7+9

Decoder Application - Half Adder

  • Using the decoder, design with OR gates.
  • A Half Adder is a basic digital circuit that performs binary addition of 2 single-bit binary numbers.
  • Its inputs are A and B (both 1 bit).
  • The outputs include Sum (S), which represents the least significant bit (LSB) of the addition, and Carry (C), which represents the most significant bit (MSB).

Truth Table & Logic Expressions for Half Adder

  • Given the inputs A1 and A0, the outputs are C and S
  • If A1 and A0 are both 0, then C and S are 0
  • If A1 is 0, while A0 is 1, then C is 0 and S is 1
  • If A1 is 1, while A0 is 0, then C is 0 and S is 1
  • If A1 and A0 are both 1, then C is 1 and S is 0
  • With the use of Boolean algebra, the equations can be expressed as: C = A0 A1, and S = A0 A1 + A0 A1
  • The size of the decoder is 2 x 4.
  • Boolean expressions can be implemented with Decoders and Gates.

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