Digital Logic Design Module 1 Quiz
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Questions and Answers

Which number system is most commonly used by humans for counting and calculation?

  • Decimal number system (correct)
  • Hexadecimal number system
  • Octal number system
  • Binary number system

What is the base value of the binary number system?

  • 8
  • 2 (correct)
  • 4
  • 16

Which number system is primarily utilized by computers for processing data?

  • Hexadecimal number system
  • Octal number system
  • Binary number system (correct)
  • Decimal number system

What is the correct term for a system that represents numbers and quantities using specific rules?

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

Which of the following number systems is based on the powers of 8?

<p>Octal number system (D)</p> Signup and view all the answers

What is the base of the binary number system?

<p>2 (B)</p> Signup and view all the answers

Which hexadecimal digit represents the decimal value 10?

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

How many unique digits does the octal number system use?

<p>8 (A)</p> Signup and view all the answers

Which decimal number is equal to the binary number 1101?

<p>13 (B)</p> Signup and view all the answers

What is the decimal equivalent of the octal number 12?

<p>10 (B)</p> Signup and view all the answers

In the context of number systems, what is the main reason computers use the binary system?

<p>It aligns with digital electronics. (A)</p> Signup and view all the answers

Which of the following is NOT a valid digit in the hexadecimal system?

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

How can the decimal number 2510 be represented in binary?

<p>110001011 (B)</p> Signup and view all the answers

What is the octal representation of the decimal number 185?

<p>(271)8 (D)</p> Signup and view all the answers

Which digit makes the octal number (778)8 invalid?

<p>8 (A)</p> Signup and view all the answers

What is the binary equivalent of the octal number (236)8?

<p>(010011110)2 (A)</p> Signup and view all the answers

What does the hexadecimal digit 'C' represent in decimal?

<p>12 (A)</p> Signup and view all the answers

How would you represent the binary number (0110111001101)2 in octal format?

<p>(156)8 (C)</p> Signup and view all the answers

What is a defining characteristic of gray code?

<p>There is only a single bit change from one code word to the next. (A)</p> Signup and view all the answers

In Binary Coded Decimal (BCD), how many total combinations are possible with four bits?

<p>16 total combinations. (B)</p> Signup and view all the answers

What does EBCDIC stand for?

<p>Extended Binary Coded Decimal Interchange Code. (A)</p> Signup and view all the answers

Which of the following is true about ASCII-8?

<p>It was developed by ANSI with extended functionality. (D)</p> Signup and view all the answers

Which character coding standard uses 16 bits to represent characters?

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

Which of these coding systems is primarily developed for alphanumeric characters?

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

What is the maximum number of characters ASCII-7 can represent?

<p>128 characters. (D)</p> Signup and view all the answers

What is the decimal equivalent of the hexadecimal number (5C7)16?

<p>1479 (D)</p> Signup and view all the answers

Which binary number is equivalent to the hexadecimal number (10A8)16?

<p>0001000010101000 (A)</p> Signup and view all the answers

What is the result of adding the binary numbers (1101)2 and (101)2?

<p>10010 (D)</p> Signup and view all the answers

What is the result of subtracting (1110)2 from (10010)2?

<p>01001 (C)</p> Signup and view all the answers

What does the 1's complement of the binary number 10011100 represent?

<p>01100011 (D)</p> Signup and view all the answers

How is the 2's complement of a binary number obtained?

<p>Flip the bits and add 1 to the least significant bit. (C)</p> Signup and view all the answers

Which of the following represents binary multiplication of (1101)2 by (101)2?

<p>100001 (D)</p> Signup and view all the answers

Which of the following is NOT a valid result when performing binary addition?

<p>1 + 0 = 0 (D)</p> Signup and view all the answers

What is the result of dividing (1001110)2 by (100)2?

<p>10011 (C)</p> Signup and view all the answers

What is the weight of the hexadecimal digit 'C' in a hexadecimal number?

<p>12 (B)</p> Signup and view all the answers

What is the decimal equivalent of the binary number (101011)2?

<p>43 (C)</p> Signup and view all the answers

When converting the binary fraction 0.1101 to decimal, what is its decimal equivalent?

<p>0.8125 (D)</p> Signup and view all the answers

Which of the following correctly represents the binary number (10011)2 in decimal?

<p>19 (B)</p> Signup and view all the answers

How do you calculate the decimal equivalent of the binary number (111001)2?

<p>57 (A)</p> Signup and view all the answers

What is the result of converting the binary number (110010)2 into decimal?

<p>50 (D)</p> Signup and view all the answers

In the binary number system, what does the digit in the second position from the right (bit 1) represent?

<p>2 (B)</p> Signup and view all the answers

What is the decimal equivalent of the binary fraction (11.011)2?

<p>3.375 (C)</p> Signup and view all the answers

Which of the following describes the base of the octal number system?

<p>8 (B)</p> Signup and view all the answers

How do you convert the decimal number 44 to binary?

<p>(101100)2 (A)</p> Signup and view all the answers

Flashcards

Octal number system base

The octal number system uses base 8, meaning it only has digits from 0 to 7.

Valid Octal Number

An octal number is valid if all its digits are between 0 and 7.

Octal to Decimal Conversion

To convert an octal number to decimal, multiply each digit by its corresponding power of 8 and sum the results.

Decimal to Octal Conversion

To convert a decimal number to octal, repeatedly divide the decimal number by 8 and record the remainders. The remainders, read from bottom to top, form the octal representation.

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Hexadecimal number system

The hexadecimal number system uses base 16, meaning it has digits 0-9 and A-F, where A=10, B=11, C=12, D=13, E=14, and F=15.

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Decimal to Binary Conversion

Transforming a decimal number into its binary equivalent using a series of repeated divisions by 2, keeping track of the remainders.

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Binary Number System

A numeral system with only the digits 0 and 1, with each digit representing a power of 2.

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Binary to Decimal Conversion

Converting a binary number into its decimal representation by multiplying each bit by its positional weight (a power of 2) and summing the results.

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Bit Weight

The power of 2 assigned to each position within a binary number.

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Least Significant Bit (LSB)

The rightmost bit in a binary number, representing the smallest power of 2.

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Binary Fraction to Decimal

Converting a binary fraction into its decimal equivalent by multiplying each bit by its positional weight (a negative power of 2) and summing the results.

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Octal Number System

A numeral system with eight digits (0-7), where each digit represents a power of 8.

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Decimal Number System

A system that uses ten digits (0-9) to represent quantities. The base of this system is 10 because it has ten digits.

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Positional Value in Number Systems

In number systems like decimal, binary, octal, and hexadecimal, each digit's position determines its value. The further right the digit, the lower its value.

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Converting Between Number Systems

Changing a number from one base to another: for example, converting a decimal number to binary, octal, or hexadecimal, or vice versa.

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Base-10 (Decimal) to Base-2 (Binary)

The process of converting a number from the base-10 (decimal) system to the base-2 (binary) system.

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Base-2 (Binary) to Base-10 (Decimal)

The process of converting a number from the base-2 (binary) system to the base-10 (decimal) system.

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What is a Number System?

A system used to represent numbers and quantities using digits, symbols, and rules. It defines how we count, perform calculations, and measure.

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What is a Number System used for?

Number systems are used to represent and manipulate numerical values, enabling calculations, measurements, and data storage.

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What are the most common number systems?

The most commonly used number systems are:

  1. Decimal (base-10): Used by humans in everyday life.
  2. Binary (base-2): Used by computers for internal operations.
  3. Octal (base-8): Used in some computer systems and programming.
  4. Hexadecimal (base-16): Used in programming and for memory addressing.
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What is the Decimal Number System?

The Decimal number system is a base-10 system using the digits 0-9. Each position represents a power of 10.

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What is the Binary Number System?

The Binary number system is a base-2 system using the digits 0 and 1. Each position represents a power of 2.

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Gray Code

A binary code where each code word differs from the previous one by only a single bit change. It is also cyclic, meaning the first and last code words also differ by a single bit.

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Hexadecimal Number System Base

The hexadecimal number system uses base 16, meaning it has 16 unique digits (0-9 and A-F).

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Non-weighted Code

A code where the bits do not have assigned weights. Each bit position does not represent a specific power of two.

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Converting Hexadecimal to Decimal

To convert a hexadecimal number to decimal, multiply each digit by its corresponding power of 16 and sum the results.

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BCD (Binary Coded Decimal)

A code where each decimal digit is represented by a 4-bit binary number. Only the first ten binary combinations (0000 to 1001) are valid.

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Hexadecimal to Binary Conversion

Each hexadecimal digit can be represented by a 4-bit binary code. Convert each digit individually and concatenate the results.

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EBCDIC (Extended Binary Coded Decimal Interchange Code)

An 8-bit binary code used for representing characters (letters, numbers, and symbols) in computers. It was developed by IBM.

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Binary Addition

Add binary digits column by column, carrying over a '1' when the sum is 2 or more.

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ASCII (American Standard Code for Information Interchange)

A standard code used for representing characters in computers. It uses 7 or 8 bits to represent characters like letters, numbers, and symbols.

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Binary Subtraction

Subtract binary digits column by column, borrowing a '2' from the next higher column when needed.

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Unicode

A standard for representing characters using 16 bits, allowing for more than 65,000 unique characters. It's essential for representing characters from various languages.

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Binary Multiplication

Multiply binary digits similar to decimal multiplication, remembering that 1x1=1 and 0x1=0.

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Binary Division

Divide binary numbers by repeatedly subtracting the divisor and keeping track of the quotient.

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1's Complement of a Binary Number

Flip all the bits in the binary number. Change 0s to 1s and 1s to 0s.

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2's Complement of a Binary Number

Take the 1's complement of the binary number and add 1 to the least significant bit.

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Gray Code

A binary code where only one bit changes between consecutive numbers, allowing smoother transitions in systems.

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Study Notes

Course Information

  • Course Name: Digital Logic Design
  • Course Code: CSCS-2522
  • Credit Hours: 3
  • Instructor: Prof. Mudassar Saleem (M.Phil. Computer Science)
  • Module #: 1

Today's Agenda

  • Importance of the subject
  • What is a number system?
  • Commonly used number systems
  • Number system conversions

Course Objectives

  • Teach fundamental concepts of classical digital design
  • Demonstrate how digital circuits are designed and analyzed
  • Familiarize students with modern hierarchy of digital hardware
  • Enlighten students on state-of-the-art computer hardware design methodologies
  • Provide a basic idea of designing and simulating logic circuits

Number Systems

  • A number system is a system for representing numbers and quantities using digits, symbols, and rules for counting, calculations, and measurements.

Commonly Used Number Systems

  • Decimal
  • Binary
  • Octal
  • Hexadecimal

Common Number Systems

System Base Symbols Used by humans? Used in computers?
Decimal 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Yes No
Binary 2 0, 1 No Yes
Octal 8 0, 1, 2, 3, 4, 5, 6, 7 No No
Hexadecimal 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F No No

Quantities/Counting (Examples)

  • Example conversions of numbers in different systems (decimal, binary, octal, hexadecimal) are shown.

Conversion Among Bases

  • Decimal ↔ Binary
  • Decimal ↔ Octal
  • Binary ↔ Hexadecimal
  • Conversion techniques are illustrated.

Quick Example

  • 2510 = 110012 = 318 = 1916
  • Examples are provided to show equivalences between different number systems.

Decimal Number System

  • Consists of digits 0 to 9
  • Base is 10
  • Used for everyday calculations.

Decimal to Decimal

  • Example conversion from one decimal to another

Decimal to Binary

  • Conversion technique is explained
  • Method for converting decimal to binary

Binary Number System

  • Uses digits 0 and 1
  • Base is 2
  • Used in digital computers
  • Example conversions of binary to decimal (and vice versa) are included

Binary to Decimal

  • Conversion technique is explained: Multiply each bit by 2n, where n is the position of the bit, and then add the results

Example (Binary to Decimal)

  • 1010112 = 4310

Binary Arithmetic

  • Rules for binary addition and subtraction

Binary Subtraction

  • Rules for binary subtraction

Binary Multiplication

  • Rules for binary multiplication

Binary Division

  • Rules for binary division

1's Complement of Binary Number

  • Change all 1s to 0s and all 0s to 1s

2's Complement of Binary Number

  • Take the 1's complement, add 1 to the least significant bit

Gray Code

  • Non-weighted binary code
  • Only one bit changes between successive codes

Encoding Schemes:

  • BCD (Binary Coded Decimal)
  • EBCDIC (Extended Binary Coded Decimal Interchange Code)
  • ASCII (American Standard Code for Information Interchange)
  • Unicode

Unicode

  • Character encoding standard supporting many languages

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Digital Logic Design - Module 1 PDF

Description

Test your understanding of number systems and their conversions in the first module of Digital Logic Design. This quiz covers the importance of the subject, commonly used number systems like decimal, binary, octal, and hexadecimal, and the principles of numerical representations.

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