Introduction to Computer Systems: Data Representation
26 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the binary representation of the decimal number 25?

  • (10101)2
  • (10001)2
  • (11001)2 (correct)
  • (11101)2

(31)8 is the octal representation of the decimal number 25.

True (A)

What is the hexadecimal representation of the decimal number 25?

(19)16

The process of converting a decimal fraction to another base involves using multiplication by the _____ of the new base.

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

Match the following decimal integers with their corresponding octal representations:

<p>25 = (31)8 12 = (14)8 16 = (20)8 8 = (10)8</p> Signup and view all the answers

What is the hexadecimal representation of the binary number 1110101100110?

<p>1D66 (C)</p> Signup and view all the answers

A hexadecimal digit can be represented as a combination of 3 bits.

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

What is the octal representation of the binary number 1111010010.01001?

<p>1722.22</p> Signup and view all the answers

The binary number 1111010010.01001 converts to hexadecimal as (____).

<p>3D2.48</p> Signup and view all the answers

Match the following representations with their binary equivalents:

<p>(1FA.4C)16 = 000111111010.01001100 (456.41)8 = 100101110.100001 (1D66)16 = 0000110110100110 (16546)8 = 110101010110000</p> Signup and view all the answers

Which of the following number systems has a base of 8?

<p>Octal Number System (D)</p> Signup and view all the answers

The binary number system uses the digits 0-1.

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

What is the base of the hexadecimal number system?

<p>16</p> Signup and view all the answers

A number in a particular base is written as: (number)_______

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

Match the following number systems with their base:

<p>Binary = 2 Decimal = 10 Octal = 8 Hexadecimal = 16</p> Signup and view all the answers

What is the decimal equivalent of the binary number (1101.01)2?

<p>13.25 (D)</p> Signup and view all the answers

In the decimal number system, the highest digit is 9.

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

How do you convert a decimal integer to another base?

<p>By using integer division by the base of the new number system.</p> Signup and view all the answers

What is the binary representation of (0.2345)10?

<p>(0.001111)2 (A)</p> Signup and view all the answers

The octal value of (0.2345)10 is (0.17004)8.

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

What is the hexadecimal representation of (0.2345)10?

<p>(0.3C08312)16</p> Signup and view all the answers

(0.625)10 converted to hexadecimal is _____ .

<p>(0.A)16</p> Signup and view all the answers

Match the decimal numbers with their correct conversions:

<p>(0.2345)10 = (0.001111)2 (234.625)10 = (11101010.101)2 (0.625)10 = (0.A)16 (7526)10 = (1D66)16</p> Signup and view all the answers

What base is used when converting decimal fractions to octal?

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

A binary number can easily be converted to octal using a shortcut method.

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

What is the purpose of the conversion process shown in the content?

<p>To convert decimal fractions to binary, octal, and hexadecimal.</p> Signup and view all the answers

Flashcards

Decimal to Binary Conversion

A method to convert a base-10 number into a base-2 number (binary).

Decimal to Octal Conversion

Converting a base-10 number to a base-8 number (octal).

Decimal to Hexadecimal Conversion

Converting a base-10 number to base-16 number (hexadecimal).

Converting Decimal Fraction to Other Bases

Converting decimal fractions to other number systems (binary, octal, hex) by multiplying by the new base.

Signup and view all the flashcards

Remainders in Conversion

The remainders in division determine the digits of the new number system in base conversion.

Signup and view all the flashcards

Number Systems

Systems used to represent numbers, each with a base or radix.

Signup and view all the flashcards

Decimal Number System

A base-10 number system using digits 0-9.

Signup and view all the flashcards

Binary Number System

A base-2 number system using digits 0 and 1, fundamental in computers.

Signup and view all the flashcards

Octal Number System

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

Signup and view all the flashcards

Hexadecimal Number System

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

Signup and view all the flashcards

Conversion between number systems

The process of changing a number from one system to another.

Signup and view all the flashcards

Base (Radix)

The number of unique symbols in a number system.

Signup and view all the flashcards

Conversion from Decimal Integer to other bases

Converting whole decimal numbers to other number system

Signup and view all the flashcards

Convert Decimal to Binary

Multiplying the decimal fraction by 2, recording the integer result and repeating until the fractional part is zero. The integers form the binary representation.

Signup and view all the flashcards

Convert Decimal to Octal

Multiply the decimal fraction by 8, recording the integer result and repeating until the fractional part is zero. The integers form the octal representation.

Signup and view all the flashcards

Convert Decimal to Hexadecimal

Multiply the decimal fraction by 16, recording integer results until the fractional part is zero. The integers form the hexadecimal representation using letter placeholders for values above 9 (A=10, B=11...F=15).

Signup and view all the flashcards

Binary to Octal Conversion

Group binary digits in sets of 3, starting from the binary point, and convert each set to its octal equivalent.

Signup and view all the flashcards

Binary to Hexadecimal Conversion

Group binary digits in sets of 4, starting from the binary point, and convert each set to its hexadecimal equivalent.

Signup and view all the flashcards

Decimal to Different Bases Conversion

A method used to represent numerical quantities in terms of different bases (like binary, octal, and hexadecimal).

Signup and view all the flashcards

Hexadecimal Digits

The digits 0-9 and A-F representing values from 0 to 15 in hexadecimal system.

Signup and view all the flashcards

Octal Digits

The digits 0-7 representing values from 0 to 7 in octal system.

Signup and view all the flashcards

Octal to Binary

Converting an octal number (base-8) to a binary number (base-2). Each octal digit is represented as a 3-bit binary sequence.

Signup and view all the flashcards

Hexadecimal to Binary

Converting a hexadecimal number (base-16) to a binary number (base-2). Each hexadecimal digit translates to a 4-bit binary sequence.

Signup and view all the flashcards

Binary to Octal

Converting a binary number (base-2) to an octal number (base-8). Group the binary digits in sets of 3, starting from the rightmost digit, and convert each group to its octal equivalent.

Signup and view all the flashcards

Binary to Hexadecimal

Converting a binary number (base-2) to a hexadecimal number (base-16). Group the binary digits in sets of 4, starting from the rightmost digit, and convert each group to its hexadecimal equivalent.

Signup and view all the flashcards

Converting Decimal Fractions

Converting decimal fractions to other bases (binary, octal, hex) by multiplying by the new base repeatedly, collecting the integer parts as the new number's fractional digits.

Signup and view all the flashcards

Study Notes

Introduction to Computer Systems: Data Representation

  • Data, in various forms (numbers, text, audio, images, video, or multimedia), needs representation within computers.
  • All data in computers is encoded using 0s and 1s.
  • Encoding describes how data is represented by 0s and 1s.
  • Computer systems primarily deal with four number systems: binary, octal, decimal, and hexadecimal.

Number Systems

  • A number system with base (radix) r uses unique symbols for r digits.
  • Digits in a base r number have:
    • Digit value
    • Position value
  • A number in base r is written as (number)r.
  • The number of values representable in n digits of base r is rn.
  • Example: Decimal (base 10) uses digits 0-9.
  • Example: (5432)10 = 5 * 103 + 4 * 102 + 3 * 101 + 2 * 100

Number System Examples

  • Binary (base 2): Uses 0 and 1.
  • Octal (base 8): Uses 0-7.
  • Decimal (base 10): Uses 0-9.
  • Hexadecimal (base 16): Uses 0-9 and A-F (A=10, B=11, C=12, D=13, E=14, F=15).

Converting Decimal to Other Bases

  • To convert a decimal integer to another base, perform successive integer divisions by the base of the new system.

  • Example: Converting (25)10 to binary (base 2).

    • Continued division yields: 25 / 2 = 12 remainder 1, 12 / 2 = 6 remainder 0, 6 / 2 = 3 remainder 0, 3 / 2 = 1 remainder 1, 1 / 2 = 0 remainder 1.
    • Reading the remainders from bottom to top gives (11001)2.

  • To convert decimal fractions, repeatedly multiply by the new base and record the integer part.

  • Example: (0.2345)10 to binary (base 2) gives .001111.

Converting Between Bases

  • Converting between different number systems (binary, octal, hexadecimal).
    • Shortcut methods exist for converting between binary, octal, and hexadecimal efficiently.
  • Group binary digits (3 for octal, 4 for hexadecimal).
    • Convert each group to its respective octal or hexadecimal equivalent.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Introduction to Computer Systems - Lecture 4 PDF

Description

Explore the fundamentals of data representation in computer systems. Understand how various number systems—binary, octal, decimal, and hexadecimal—encode information using 0s and 1s. This quiz will test your knowledge of these key concepts in data encoding and number systems.

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser