Digital Logic Design - Booth's Algorithm
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Questions and Answers

What is the result of multiplying 7 by 3 using Booth's Algorithm?

  • 20
  • 21 (correct)
  • 24
  • 18

Which step is NOT typically part of Booth's Algorithm when performing signed binary multiplication?

  • Performing a two's complement operation
  • Converting the result into decimal (correct)
  • Initializing the multiplicand and multiplier
  • Completing the binary addition

In Booth's Algorithm, what is the purpose of using two's complement?

  • To convert the binary result into decimal
  • To modify the multiplicand before multiplication
  • To represent negative numbers in binary form (correct)
  • To simplify the multiplication process by reducing the number of operations

Which of the following is true about signed binary multiplication?

<p>It utilizes a specific algorithm for efficient computation. (C)</p> Signup and view all the answers

What is the primary advantage of using Booth's Algorithm for signed binary multiplication?

<p>It simplifies the handling of both positive and negative factors. (B)</p> Signup and view all the answers

What does the control signal mode M determine in a binary adder/subtractor?

<p>The operation performed (addition or subtraction) (C)</p> Signup and view all the answers

In the binary adder diagram, what does the output S represent?

<p>The result of the addition or subtraction computation (C)</p> Signup and view all the answers

What is the role of the carry input Ci in the binary adder/subtractor?

<p>To provide an initial carry for addition (B)</p> Signup and view all the answers

What is the primary difference between SRAM and DRAM?

<p>SRAM retains data without needing constant refresh. (D)</p> Signup and view all the answers

Which memory type is primarily used for cache memory?

<p>SRAM (B)</p> Signup and view all the answers

If M=1 in the binary adder/subtractor, what operation is being performed?

<p>Subtraction only (A)</p> Signup and view all the answers

What will be the result F when the binary adder/subtractor receives inputs x=4 and y=2, and M=0?

<p>6 (C)</p> Signup and view all the answers

What feature is true of DRAM compared to SRAM?

<p>DRAM uses a capacitor to store data. (A)</p> Signup and view all the answers

Which statement about cache memory is correct?

<p>Cache memory speeds up access to frequently used data. (D)</p> Signup and view all the answers

Which is a characteristic of SRAM?

<p>SRAM generally offers lower density than DRAM. (C)</p> Signup and view all the answers

What is the primary function of the ALU in the SAP-1?

<p>To execute arithmetical operations (A)</p> Signup and view all the answers

Which register is mentioned as part of the ALU in the SAP-1?

<p>Accumulator (AC) (A)</p> Signup and view all the answers

What type of operations can the ALU perform in the SAP-1 system?

<p>Both arithmetical and logical operations (A)</p> Signup and view all the answers

How many registers does the ALU include for executing operations in the SAP-1?

<p>Two registers including AC (C)</p> Signup and view all the answers

In the context of the SAP-1, what role does the 'another register' serve in the ALU?

<p>It is involved in executing calculations alongside the AC (D)</p> Signup and view all the answers

What happens during the T5 state regarding 𝐶𝐸 and 𝐿𝐴?

<p>Both 𝐶𝐸 and 𝐿𝐴 are active. (C)</p> Signup and view all the answers

What does the operation M[MAR]→A signify during the T5 state?

<p>Data is being transferred from MAR to A. (B)</p> Signup and view all the answers

What is the function of the T6 state in the LDA routine?

<p>It executes a no operation (nop). (C)</p> Signup and view all the answers

Which clock edge is involved in the action M[MAR]→A?

<p>Positive clock edge. (C)</p> Signup and view all the answers

During which state are 𝐶𝐸 and 𝐿𝐴 both confirmed to be active?

<p>T5 state. (D)</p> Signup and view all the answers

What operation does the instruction 'M[MAR]→IR' perform in the SAP 1 architecture?

<p>It writes the contents of the MAR into the Instruction Register. (D)</p> Signup and view all the answers

In the SAP 1 architecture, what does 'AC+B→AC' signify?

<p>The value in AC is replaced by the addition of AC and B. (B)</p> Signup and view all the answers

What does the 'PC→MAR' instruction achieve in the sequence?

<p>It copies the contents of the Program Counter to the Memory Address Register. (C)</p> Signup and view all the answers

Which operation occurs immediately after 'IR[4-15]→ MAR' in the SAP 1 architecture?

<p>Contents are fetched from the memory location specified by MAR. (A)</p> Signup and view all the answers

What does 'PC+1→PC' represent in the context of SAP 1 architecture?

<p>It updates the Program Counter to point to the next instruction in sequence. (D)</p> Signup and view all the answers

Flashcards

Binary Adder/Subtractor

A digital circuit that performs the addition and subtraction of binary numbers.

M (Mode Signal)

The control signal in a binary adder/subtractor circuit that determines whether to add or subtract.

x & y

The input lines to the binary adder/subtractor circuit representing the numbers to be added or subtracted.

F (Result)

The output lines representing the result of the addition or subtraction operation.

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Ci (Carry-in) & Cy (Carry-out)

The carry-in and carry-out signals in the binary adder/subtractor circuit.

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Booth's Algorithm

A method of multiplying numbers in binary format, specifically designed for signed numbers.

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Bit-by-bit Examination

In Booth's algorithm, the multiplier is examined bit by bit, starting from the least significant bit. Based on the current bit and the previous bit, different operations are performed on the multiplicand.

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Multiplication Operations

During Booth's Algorithm, depending on the bits being analyzed, three possibilities arise:

  1. 01: The multiplicand is added to the product.
  2. 10: The multiplicand is subtracted from the product.
  3. 00 or 11: No operation is performed.
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Product Shifting

The product is shifted one position to the left after each iteration of examining a pair of multiplier bits.

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Final Iteration

The final iteration of the process, after examining all the bits of the multiplier, yields the final multiplication result.

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What is the role of the Program Counter (PC)?

Program Counter (PC) holds the address of the next instruction to be executed.

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What is the Memory Address Register (MAR) for?

Memory Address Register (MAR) stores the address of the memory location to be accessed.

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What does the Instruction Register (IR) contain?

Instruction Register (IR) holds the instruction fetched from memory.

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What is the difference between the opcode and operand in an instruction?

The instruction's opcode (operation code) is used to determine the operation to be performed. The operand specifies the data or address to be used in the operation.

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What is the purpose of the Accumulator (AC)?

The Accumulator (AC) acts as a temporary storage location for intermediate results during calculations.

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Arithmetic Logic Unit (ALU)

The part of a computer's central processing unit (CPU) that performs arithmetic and logical operations. It manipulates binary data to execute instructions.

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Accumulator (AC)

A register within the ALU that temporarily stores the result of an arithmetic or logical operation before it is written back to memory.

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ALU Register

A specialized register within the ALU that helps in executing arithmetic operations. It might hold one of the operands or intermediate results.

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Arithmetical Operations

Specific instructions for performing various mathematical operations like addition, subtraction, multiplication, or division. The ALU uses these instructions to manipulate data.

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T5 State in LDA Routine

During the T5 state of the LDA routine, the control signals CE (Chip Enable) and LA (Load A) are activated, triggering the transfer of data from the Memory (M) to the Accumulator (A) on the rising edge of the clock signal.

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T6 State in LDA Routine

The T6 state in the LDA routine is a 'no operation' (nop) state, meaning that no action is performed, and the system remains idle.

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M[MAR]→A

The notation 'M[MAR]→A' represents the transfer of data from the memory location addressed by the Memory Address Register (MAR) to the accumulator (A).

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Chip Enable (CE)

The Chip Enable (CE) signal controls whether the memory chip is active and ready to receive or transmit data. When 'active', the chip is ready for operations.

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Load A (LA)

The Load A (LA) signal determines whether the content from a register or source should be loaded into the accumulator (A).

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SRAM vs DRAM

SRAM uses latches to store data, making it faster but more expensive and consuming more power. DRAM uses capacitors to store data, making it slower but cheaper and less power-hungry.

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Cache Memory

A cache is a smaller, faster memory that stores frequently used data, speeding up access times.

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Principle of Locality

The principle of locality states that data accessed recently or close to currently accessed data will likely be needed again.

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Spatial & Temporal Locality

Spatial locality refers to accessing data near the current location, while temporal locality refers to accessing data recently accessed.

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Memory System Components

A memory system comprises RAM, cache, and secondary storage. It manages the flow of data between these components.

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Study Notes

Computer Architecture 2024/2025

  • Course offered by Dr. Elmahdy Maree
  • Academic year 2024/2025
  • Lecture 1 is covered

Learning Objectives

  • Students will be able to describe the design of digital building blocks

Introduction to Computer Architecture and Organization

  • Computer architecture refers to programmer-visible attributes of a system that impact program execution
    • Includes instruction set, number of data types (e.g., numbers, characters), I/O mechanisms, and addressing techniques
  • Computer organization refers to the operational units and their interconnections, realizing architectural specifications
    • Includes hardware details that are transparent to the programmer, such as control signals, interfaces between computer and peripherals, memory technology

Digital Building Blocks (Registers, Counters)

  • Registers are computer memory built into the CPU for storing and manipulating data during instruction execution
    • Can hold instructions, storage addresses, or data
  • Buffer Registers
    • Registers directly built into processor/CPU also used to store and manipulate data while executing instruction, these may also hold an instruction, a storage address, or any kind of data
    • Diagram shows different kinds of buffer register including a controlled buffer register, and hardware implementation showing internal components
  • Three-State Registers
    • A normally open switch & a normally closed switch diagrams are shown, explaining the symbol and function of these, also tables showing the operation of such a switch in a three state buffer register
  • Shift Registers
    • Diagrams show the structure of shift-left and shift-right registers
  • Bus-Organized Computers
    • A bus is a group of wires that transmit a binary word
    • Diagrams show bus-organized computer components and their interconnections.

Review of Flip Flops

  • Covers characteristics and excitation tables for D, T, and JK flip-flops

Computer Components: Top-Level View

  • A diagram showing the key components of a computer system
    • CPU, main memory, I/O module, and the system bus
    • Specific registers are identified, including PC, IR, MAR, MBR, I/O AR, I/O BR
  • IAS stands for Princeton Institute for Advanced Studies (Von Neumann architecture)

Counters

  • Synchronous Counters: Detailed discussion of their design and functionality.
  • Asynchronous (Ripple) Counters: Detailed discussion of their design and functionality.
  • Diagrams and examples show how these counters work, including characteristic and excitation tables

ROM and RAM Design

  • ROM (Read-Only Memory): Describes different ROM types including mask programmable ROM, programmable ROM (PROM), erasable programmable ROM (EPROM), and electric-erasable programmable ROM (EEPROM).
  • RAM (Random Access Memory): Details on RAM design.
  • Memory System covers ROM and RAM components in a computer system.
  • Diagrams of different types of ROM and RAM chips are presented showing internal components

Cache Memory

  • Definition of cache memory, its location, and function in a computer system as an intermediate storage area for frequently used data
  • Memory hierarchy is presented as a pyramid illustrating the different levels of memory in a computer from fastest to slowest

More Details of Computer Components

  • Diagrams and tables are shown explaining the different parts of a computer system and components.

Questions

  • A section for questions are included in the slides

Additional Information

  • Included in the presentation slides on computer architecture.

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Lecture 1 - Computer Architecture-مدمج PDF

Description

This quiz covers essential concepts related to Booth's Algorithm and binary arithmetic operations. Test your knowledge on signed binary multiplication, differences between memory types, and the workings of binary adders. Perfect for students studying digital logic design and binary systems.

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