Four-Variable K-Map Overview
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Questions and Answers

What happens when two inputs of an encoder are active at the same time?

  • The output will represent both inputs combined.
  • The output becomes 111 for both inputs.
  • The output generates an undefined combination. (correct)
  • The output defaults to the highest priority input output.

    • How does a priority encoder resolve input ambiguities?

  • It prioritizes the input with the highest value.
  • It equally weights all inputs.
  • It ignores any signals that conflict.
  • It establishes a hierarchy by assigning priorities to inputs. (correct)

    • What does the output V indicate in a priority encoder?

  • It displays the total number of active inputs.
  • It provides a binary representation of the input.
  • It reflects the highest priority input's value.
  • It shows if any input is equal to 1. (correct)

    • If input D3 is active, what output will a four-input priority encoder produce?

    <p>11</p> Signup and view all the answers

    What is the output of a priority encoder when all inputs are inactive?

    <p>Output V is set to 0.</p> Signup and view all the answers

    What does the encoder output when both D3 and D6 are active at the same time, assuming a priority for higher subscripts?

    <p>110</p> Signup and view all the answers

    In a priority encoder, what will happen if D2 is active while D3 is inactive?

    <p>Output will be 10.</p> Signup and view all the answers

    How do encoder circuits prevent generating the same output for different input conditions?

    <p>By establishing input priorities.</p> Signup and view all the answers

    What does each square in a four-variable K-map represent?

    <p>One minterm with four literals</p> Signup and view all the answers

    How are the rows and columns of a four-variable K-map numbered?

    <p>Using a Gray code sequence</p> Signup and view all the answers

    Which of these minterms corresponds to the square in the third row and second column of the K-map?

    <p>m13</p> Signup and view all the answers

    What is the result of combining eight adjacent squares in a K-map?

    <p>A term with one literal</p> Signup and view all the answers

    If a function F(w, x, y, z) is defined by minterms that include m0, m1, and m2, what can be concluded?

    <p>These minterms can be simplified in a K-map</p> Signup and view all the answers

    What will combining two adjacent squares yield in a four-variable K-map?

    <p>A simplified term with two literals</p> Signup and view all the answers

    What is the significance of combining adjacent squares in a K-map?

    <p>It helps simplify the function</p> Signup and view all the answers

    What does the term w'z' represent when using a K-map?

    <p>Combining two rows and two columns</p> Signup and view all the answers

    What condition allows the D latch to store the value on the D pin?

    <p>When En is HIGH</p> Signup and view all the answers

    What is a key difference between a latch and a flip-flop?

    <p>Latches are asynchronous, while flip-flops are edge-triggered.</p> Signup and view all the answers

    Which of the following inputs causes the Q output of a D latch to reset to 0?

    <p>When D is LOW and En is HIGH</p> Signup and view all the answers

    What occurs when both inputs S and R of the SR latch are equal to 1?

    <p>The latch enters an indeterminate state.</p> Signup and view all the answers

    What role does the inverter play in a D flip-flop?

    <p>It enables the slave latch during the clock cycle.</p> Signup and view all the answers

    How does a D flip-flop change its output state?

    <p>Only at the negative edge of the clock signal</p> Signup and view all the answers

    Which state is the D latch in when En is set to 0?

    <p>The latch cannot change state.</p> Signup and view all the answers

    When does the master latch in a D flip-flop store input data from the D line?

    <p>At the falling edge of the clock</p> Signup and view all the answers

    What is the primary function of secondary storage in a computer system?

    <p>Retain information when power is turned off.</p> Signup and view all the answers

    Which of the following accurately describes the access times for secondary storage compared to primary memory?

    <p>They are longer for secondary storage.</p> Signup and view all the answers

    What component performs arithmetic and logic operations in a computer?

    <p>Arithmetic and Logic Unit (ALU).</p> Signup and view all the answers

    Which type of storage is faster in accessing data than secondary storage?

    <p>Registers.</p> Signup and view all the answers

    What is the primary role of the output unit in a computer system?

    <p>To send processed results to the outside world.</p> Signup and view all the answers

    Which of the following is NOT a type of secondary storage device?

    <p>Graphic displays.</p> Signup and view all the answers

    What happens to operands before an arithmetic operation is performed in the ALU?

    <p>They are brought into the processor and stored in registers.</p> Signup and view all the answers

    Which component generates output in the form of printed documents?

    <p>Output unit.</p> Signup and view all the answers

    What is the result in Register R0 after executing the instruction 'Add LOCA, R0'?

    <p>45H</p> Signup and view all the answers

    What is the first step in the execution of an instruction?

    <p>Fetch the instruction from memory into the IR.</p> Signup and view all the answers

    Which of the following is true about the instruction 'Add R1, R2, R3'?

    <p>R3 will contain the sum of R1 and R2.</p> Signup and view all the answers

    What does 'LOCA' represent in the instruction 'Add LOCA, R0'?

    <p>A memory operand.</p> Signup and view all the answers

    What will be the value of R3 after executing 'Add R1, R2, R3' if R1 = 24H and R2 = 34H?

    <p>58H</p> Signup and view all the answers

    How is the result from 'Add LOCA, R0' ultimately stored?

    <p>In Register R0.</p> Signup and view all the answers

    What is the immediate effect on LOCA after the instruction 'Add LOCA, R0' is executed?

    <p>It remains unchanged.</p> Signup and view all the answers

    In the context of these instructions, what does the term 'Opcode' refer to?

    <p>The operation code that specifies the operation to be performed.</p> Signup and view all the answers

    Study Notes

    Four-Variable K-Map

    • A four-variable K-map represents Boolean functions using variables w, x, y, z across 16 minterms.
    • Each minterm corresponds to a square in the K-map, determined by concatenating row and column numbers in Gray code.
    • Minterms can be combined to simplify Boolean expressions:
      • One square = four literals
      • Two adjacent squares = three literals
      • Four adjacent squares = two literals
      • Eight adjacent squares = one literal
      • Sixteen squares represent a constant function (1).
    • Example function F(w, x, y, z) = Σm(0, 1, 2, 4, 5, 6, 8, 9, 12, 13, 14) simplifies to y' and w'z' among others through adjacency.

    Encoder Circuit

    • An encoder converts multiple inputs into a binary representation, often facing ambiguities when multiple inputs are active.
    • Priority encoders resolve ambiguities by assigning priority levels to inputs, ensuring only the highest priority input is encoded.
    • The valid bit output (V) indicates if any input is active, preventing confusion when no input is present.
    • Outputs for input D3 (highest priority), D2, and D1 change based on the presence of higher priority inputs, establishing clear state outputs.

    D Latch and Flip-Flops

    • A D latch stores binary data (1 or 0) based on the D (data) and En (enable) inputs, eliminating indeterminacy.
    • Flip-flops are bistable multivibrators crucial for digital electronics, driven by clock signals for edge-triggered state changes.
    • A D flip-flop structure consists of two D latches (master/slave), where data transfer occurs at a negative clock edge.

    Secondary Storage

    • Secondary storage complements primary memory by providing less expensive, permanent solutions for large data sets.
    • Types include magnetic disks, optical disks, and flash memory, with slower access times but essential for infrequently accessed data.

    Arithmetic and Logic Unit (ALU)

    • The ALU performs arithmetic and logical operations crucial for processing tasks within the computer.
    • Operands must be brought into the processor from memory for operations like addition or comparison, with results stored back in memory or registers.
    • Registers are high-speed storage elements used to hold operands temporarily, enabling fast access compared to cache memory.

    Output Unit

    • The output unit functions to transfer processed data to external devices, such as printers and displays.
    • Printers, categorized as either laser or inkjet, output physically, albeit at slower rates than electronic processes.

    Steps for Instruction Execution

    • Instructions follow an opcode format and specify source and destination operands.
    • Example step sequence involves fetching the instruction, decoding it, accessing memory/registers, performing operations, and storing results.
    • Operations can involve both memory locations and registers, with specific actions dictated by the opcode.

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    Description

    This quiz focuses on the four-variable K-map used in Boolean functions, specifically examining the relationship between inputs w, x, y, and z. It covers the 16 minterms and utilizes Grey code to simplify the map layout while highlighting the significance of adjacent squares. Test your understanding of K-maps and their application in digital logic design.

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