Digital Logic and Number Systems

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Questions and Answers

Which of the following is the correct order of steps when converting a Boolean function to a SOP circuit?

  • K-map -> Truth table -> Minimized function -> SOP circuit
  • Minimized function -> Truth table -> K-map -> SOP circuit
  • Truth table -> K-map -> Minimized function -> SOP circuit (correct)
  • Truth table -> Minimized Function -> K-map -> SOP circuit

A mistake in creating the truth table will not affect the grading of the K-map derived from it.

False (B)

What is the primary difference between a Moore and a Mealy circuit?

  • Mealy circuits are synchronous, while Moore circuits are asynchronous.
  • Moore circuits have outputs that depend only on the current state, while Mealy circuits' outputs depend on both the current state and input. (correct)
  • Moore circuits use only D flip-flops, while Mealy circuits use only JK flip-flops.
  • Mealy circuits have outputs that depend only on the current state, while Moore circuits' outputs depend on both the current state and input.

What is 'sign extension' when comparing two's complement binary numbers of different bit sizes?

<p>Sign extension involves extending the sign bit (most significant bit) of the smaller number to match the bit size of the larger number, preserving its numeric value and sign.</p>
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Which of the following operations is commonly used to perform multiplication or division by powers of 2?

<p>Shifting bits (D)</p>
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The process of retrieving an instruction from memory is part of the ________ stage in the fetch-decode-execute cycle.

<p>fetch</p>
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Match the following number representations with their correct descriptions:

<p>Sign-Magnitude = Represents numbers with a sign bit and magnitude. 1s Complement = Represents negative numbers by inverting all bits of the positive number. 2s Complement = Represents negative numbers by inverting all bits and adding 1 to the result.</p>
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In MIPS assembly, what type of instruction is used to move data from memory to a register?

<p><code>load</code> (D)</p>
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System services in MIPS can be used for both reading input and printing output.

<p>True (A)</p>
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When calling a subroutine in MIPS, where are arguments commonly passed?

<p>In registers (C)</p>
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Explain the purpose of pushing a register onto the stack.

<p>Pushing a register onto the stack saves its value, typically before calling a subroutine, so its contents can be restored later.</p>
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What is the purpose of Cyclic Redundancy Check (CRC)?

<p>Error detection (C)</p>
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A Hamming code can always detect and correct any single-bit error in a data transmission or storage.

<p>False (B)</p>
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What does DMA stand for in the context of I/O?

<p>Direct Memory Access (B)</p>
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Name one of the common cache replacement policies.

<p>LRU (Least Recently Used)</p>
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Which of the following is a key service provided by an operating system?

<p>Resource Management (D)</p>
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In a __________ Operating System, the kernel provides minimal services, and most operating system services are implemented in user-level programs.

<p>microkernel</p>
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Match the following RAID levels with their descriptions:

<p>RAID 0 = Striping; provides increased performance but no redundancy. RAID 1 = Mirroring; provides redundancy by duplicating data on multiple drives. RAID 5 = Striping with parity; protection against a single drive failure.</p>
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Interpreted languages generally execute faster than compiled languages because they are run directly without an intermediate compilation step.

<p>False (B)</p>
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Which characteristic best describes assembly programs that calculate parity using rotations?

<p>Rotation puts the right-most bit in the sign bit, where it can be tested. (A)</p>
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Flashcards

Truth Table

A table listing all possible input combinations and their corresponding output values for a Boolean function.

Karnaugh Map (K-map)

A visual method used to simplify Boolean algebra expressions and reduce the number of gates needed in a digital circuit.

Sum of Products (SOP)

A digital circuit design approach where the output is the logical sum of products of the input variables.

State Table (Flip-Flop)

A table that shows the next state of a flip-flop based on its current state and input.

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Combinational Circuits

Digital circuits whose output depends only on the current input values.

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Sequential Circuits

Digital circuits whose output depends on both the current input and the past sequence of inputs (stored state).

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Flip-Flop

Elementary building block of sequential circuits that can store one bit of information.

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Sign-Magnitude Form

Represents a number by its sign (positive or negative) and magnitude (absolute value).

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1's Complement

Formed by inverting all the bits of a binary number.

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2's Complement

Formed by adding 1 to the 1's complement of a binary number.

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Sign Extension

The process of extending the sign bit of a signed binary number to the left, to maintain its numeric value when represented with more bits.

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ASCII Code

A standard for representing characters where each character is assigned a unique 7-bit code.

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Decimal-Hex Conversion

Converting a number from base-10 (decimal) to base-16 (hexadecimal) or vice versa.

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IEEE Floating Point Format

A technical standard for floating-point arithmetic, defining how numbers are stored and computed in computers.

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Fetch-Decode-Execute Cycle

The fundamental operational process of a computer, which includes fetching instructions, decoding them, and executing them in sequence.

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Load (MIPS)

A programming language command that moves data from memory to a register.

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Store (MIPS)

A programming language command that moves data from a register to memory.

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Loop (MIPS)

A block of code that repeats a set of instructions until a certain condition is met.

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Subroutine

A self-contained block of code that performs a specific task; it can be called from different parts of a program.

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Stack

A data structure that follows the Last-In-First-Out (LIFO) principle, used for temporary storage and retrieval of data.

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Study Notes

  • There is a multi-part problem involving a Boolean function
    • Create a truth table.
    • Create a K-map and find the minimized function.
    • Draw a SOP circuit from the minimized function.
  • Mistakes in one part will not necessarily affect the grading of other parts.
  • Construct a state table for a flip-flop.
  • Construct a Moore or Mealy circuit based on a flip-flop.
  • Explain the difference between combinational and sequential circuits.
  • Explain what differentiates a flip-flop from other sequential circuits.
  • Represent positive and negative numbers in:
    • Sign-Magnitude form
    • 1s Complement
    • 2s Complement
  • Convert between binary and decimal representations.
  • Compare 2s complement binary numbers of different bit sizes, considering sign extension.
  • Add 2s complement binary numbers.
  • Divide or multiply numbers using bit shifting.
  • Interpret ASCII codes using a reference table.
  • Convert between decimal, hexadecimal, and binary number systems.
  • Convert a decimal fraction to binary and then to IEEE floating-point format. Perform floating-point addition or multiplication.
  • Describe the fetch-decode-execute cycle.
  • Write single statements using load or store MIPS commands, with a MIPS reference provided.
  • Write a loop in MIPS and use system services for reading and/or printing.
  • Call a subroutine in MIPS, passing values in registers.
  • Push a register to the stack and pop a register from the stack in MIPS.
  • Create or decipher a CRC to determine data integrity.
  • Construct or decipher a Hamming Code to detect and correct errors.
  • Determine addressing formats for cache memory and decipher memory addresses.
  • Know cache replacement policies.
  • Understand and discuss the different types of I/O: programmed, interrupt, memory-mapped, DMA, and I/O channel.
  • Know the 8 RAID levels.
  • Know the services an OS provides.
  • Know the difference between monolithic and microkernel Operating Systems.
  • Know the difference between interpreted and compiled programming languages.
  • Know the generations of computer languages and describe them.

Extra Credit Problem

  • Write an assembly language program fragment using ROR (rotate bits to the right).
  • The program will count the number of '1' bits in register $s0 using rotations.
  • Register $s1 should contain the resulting count (0-32)
  • Register $s0 should retain its original value.
  • Determine if the parity is odd or even and store '1' for odd or '0' for even in register $s1.
  • The solution should be a fragment without needing a data section or exit syscall.

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