Binary and Number Systems Quiz

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Questions and Answers

What is the decimal equivalent of the binary number (11011)_2?

  • 13351
  • 27 (correct)
  • 2727
  • 38

What is the binary equivalent of the decimal number (23)_10?

  • 10111 (correct)
  • 11111
  • 11000
  • 1101

Which of these is a valid binary number?

  • 10010110 (correct)
  • 20010110
  • 11031011
  • 100101102

What is the octal equivalent of the binary number (101101)_2?

<p>131 (B)</p> Signup and view all the answers

Perform the following binary multiplication: (101)_2 * (11)_2 ?

<p>1111 (C)</p> Signup and view all the answers

What is the decimal equivalent of the octal number (734)_8?

<p>476 (C)</p> Signup and view all the answers

Which of these binary numbers represents the decimal number (15)_10?

<p>1111 (D)</p> Signup and view all the answers

What is the hexadecimal equivalent of the decimal number (29)_10?

<p>1D (A)</p> Signup and view all the answers

What is the octal representation of the binary number 101101?

<p>155 (A)</p> Signup and view all the answers

Which of the following correctly represents the 9's complement of the decimal number 3245?

<p>6754 (B)</p> Signup and view all the answers

In the context of binary numbers, what is the 1's complement of 10101?

<p>01010 (C)</p> Signup and view all the answers

Why is the octal or hexadecimal representation more desirable for humans when communicating about binary numbers?

<p>They require fewer digits to represent the same binary number. (C)</p> Signup and view all the answers

In the context of the 9's complement, what does the expression "10^n - 1" represent?

<p>A number with n consecutive 9s. (C)</p> Signup and view all the answers

What is the main advantage of using complements in digital computers?

<p>To simplify the subtraction operation. (B)</p> Signup and view all the answers

What is the relationship between the radix complement and the diminished radix complement?

<p>The radix complement is always one more than the diminished radix complement. (D)</p> Signup and view all the answers

Which of the following BEST describes the goal of using octal or hexadecimal representations for binary numbers?

<p>To make it easier for humans to understand and work with binary data. (B)</p> Signup and view all the answers

What is the binary representation of the decimal number 13?

<p>1101 (C)</p> Signup and view all the answers

Which of the following numbers is not a valid octal number?

<p>256 (B)</p> Signup and view all the answers

What is the 2's complement of the binary number 1010?

<p>0110 (C)</p> Signup and view all the answers

What is the result of the Boolean expression A * B' + C when A = 1, B = 0, and C = 1?

<p>1 (A)</p> Signup and view all the answers

Which of the following is NOT a basic logic gate?

<p>XOR (D)</p> Signup and view all the answers

What is the simplified Boolean expression for the expression A'B + AB' + AB?

<p>A + B (C)</p> Signup and view all the answers

Which of the following properties is TRUE for the Boolean AND operation?

<p>All of the above (D)</p> Signup and view all the answers

In Boolean Algebra, what is the value of 1 + 0?

<p>1 (A)</p> Signup and view all the answers

What is the output of a NOT gate when the input is 0?

<p>1 (D)</p> Signup and view all the answers

Flashcards

Digital Computers

Computers that process data in binary form.

Binary System

A numbering system using only two digits, 0 and 1.

Number Base Conversion

Changing numbers from one base to another (e.g., decimal to binary).

Octal Numbers

A base-8 number system using digits 0-7.

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Hexadecimal Numbers

A base-16 system using digits 0-9 and letters A-F.

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Boolean Algebra

A branch of algebra where values are true or false, often represented with 1 and 0.

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Logic Gates

Devices that perform basic logical functions in a circuit.

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Adders

Combinational circuits that perform addition of binary numbers.

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Registers

Small storage locations in a CPU for quick data access.

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Synchronous Sequential Logic

Circuits that change states at specific intervals, controlled by a clock.

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Binary Number System

A system using only two digits, 0 and 1, for representation.

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Binary Addition

Combining two binary numbers to produce a sum using base 2 rules.

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Binary Subtraction

Subtracting binary numbers with borrowing rules specific to base 2.

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Binary Multiplication

Multiplying binary numbers by applying rules of base 2, where digits are 0 or 1.

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Base Conversion

Changing a number from one base to another, like binary to decimal.

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Decimal to Binary Conversion

Process of converting decimal numbers to binary by separating into integer and fraction parts.

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Octal Number System

A numeric system using base 8, represented by digits 0-7.

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Example of Decimal to Octal

Converting decimal 408.5 to octal by multiplying and adding powers of 8.

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Octal System

A number system with base 8 using digits 0-7.

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Hexadecimal System

A base-16 number system, using digits 0-9 and A-F.

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9's Complement

The (9's complement) subtracts each digit from 9 for decimal numbers.

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1's Complement

The (1's complement) subtracts a binary number from a string of 1's.

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Radix Complement

The r's complement method for subtraction in base r systems.

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Diminished Radix Complement

The (r-1)'s complement is used to simplify subtraction in each base.

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Compact Number Representation

Using octal or hexadecimal to reduce digit count compared to binary.

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Study Notes

Book Title and Author

  • Digital Logic and Computer Design
  • M. Morris Mano

Contents

  • Preface
  • Binary Systems (Chapter 1)
    • Digital Computers and Digital Systems
    • Binary Numbers
    • Number Base Conversions
    • Octal and Hexadecimal Numbers
    • Complements
    • Signed Binary Numbers
    • Binary Codes
    • Binary Storage and Registers
    • Binary Logic
    • References
    • Problems
  • Boolean Algebra and Logic Gates (Chapter 2)
    • Basic Definitions
    • Axiomatic Definition of Boolean Algebra
    • Basic Theorems and Properties of Boolean Algebra
    • References
    • Problems
  • Simplification of Boolean Functions (Chapter 3)
    • The Map Method
    • Two- and Three-Variable Maps
    • Four-Variable Map
    • Five-Variable Map
    • Product of Sums Simplification
    • NAND and NOR Implementation
    • Other Two-Level Implementations
    • Don't-Care Conditions
    • The Tabulation Method
    • Determination of Prime Implicants
    • Selection of Prime Implicants
    • Concluding Remarks
    • References
    • Problems
  • Combinational Logic (Chapter 4)
    • Introduction
    • Design Procedure
    • Adders
    • Subtractors
    • Code Conversion
    • Analysis Procedure
    • Multilevel NAND Circuits
    • Multilevel NOR Circuits
    • Exclusive-OR Functions
    • References
    • Problems
  • MSI and PLD Components (Chapter 5)
    • Introduction
    • Binary Adder and Subtractor
    • Decimal Adder
    • Magnitude Comparator
    • Decoders and Encoders
    • Multiplexers
    • Read-Only Memory (ROM)
    • Programmable Logic Array (PLA)
    • Programmable Array Logic (PAL)
    • References
    • Problems
  • Synchronous Sequential Logic (Chapter 6)
    • Introduction
    • Flip-Flops
    • Triggering of Flip-Flops
    • Analysis of Clocked Sequential Circuits
    • State Reduction and Assignment
    • Flip-Flop Excitation Tables
    • Design Procedure
    • Design of Counters
    • References
    • Problems
  • Registers, Counters, and the Memory Unit (Chapter 7)
    • Introduction
    • Registers
    • Shift Registers
    • Ripple Counters
    • Synchronous Counters
    • Timing Sequences
    • Random-Access Memory (RAM)
    • Memory Decoding
    • Error-Correcting Codes
    • References
    • Problems
  • Algorithmic State Machines (ASM) (Chapter 8)
    • Introduction
    • ASM Chart
    • Timing Considerations
    • Control Implementation
    • Design with Multiplexers
    • PLA Control
    • References
    • Problems
  • Asynchronous Sequential Logic (Chapter 9)
    • Introduction
    • Analysis Procedure
    • Circuits with Latches
    • Design Procedure
    • Reduction of State and Flow Tables
    • Race-Free State Assignment
    • Hazards
    • Design Example
    • References
    • Problems
  • Digital Integrated Circuits (Chapter 10)
    • Introduction
    • Special Characteristics
    • Bipolar-Transistor Characteristics
    • RTL and DTL Circuits
    • Transistor-Transistor Logic (TTL)
    • Emmitter-Coupled Logic (ECL)
    • Metal-Oxide Semiconductor (MOS)
    • Complementary MOS (CMOS)
    • CMOS Transmission Gate Circuits
    • References
    • Problems
  • Laboratory Experiments (Chapter 11)
    • Introduction to Experiments
    • Binary and Decimal Numbers
    • Digital Logic Gates
    • Simplification of Boolean Functions
    • Combinational Circuits
    • Code Converters
    • Design with Multiplexers
    • Adders and Subtractors
    • Flip-Flops
    • Sequential Circuits
    • Counters
    • Shift Registers
    • Serial Addition
    • Memory Unit
    • Lamp Handball
    • Clock-Pulse Generator
    • Parallel Adder
    • Binary Multiplier
    • Asynchronous Sequential Circuits
  • Standard Graphic Symbols (Chapter 12)
    • Rectangluar-Shape Symbols
    • Qualifying Symbols
    • Dependency Notation
    • Symbols for Combinational Elements
    • Symbols for Flip-Flops
    • Symbols for Registers
    • Symbols for Counters
    • Symbol for RAM
    • References
    • Problems
  • Appendix: Answers to Selected Problems
  • Index
  • Additional Information (Preface)

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