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Questions and Answers
What is the binary representation of the decimal number 25?
What is the binary representation of the decimal number 25?
(31)8 is the octal representation of the decimal number 25.
(31)8 is the octal representation of the decimal number 25.
True
What is the hexadecimal representation of the decimal number 25?
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.
The process of converting a decimal fraction to another base involves using multiplication by the _____ of the new base.
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Match the following decimal integers with their corresponding octal representations:
Match the following decimal integers with their corresponding octal representations:
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What is the hexadecimal representation of the binary number 1110101100110?
What is the hexadecimal representation of the binary number 1110101100110?
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A hexadecimal digit can be represented as a combination of 3 bits.
A hexadecimal digit can be represented as a combination of 3 bits.
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What is the octal representation of the binary number 1111010010.01001?
What is the octal representation of the binary number 1111010010.01001?
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The binary number 1111010010.01001 converts to hexadecimal as (____).
The binary number 1111010010.01001 converts to hexadecimal as (____).
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Match the following representations with their binary equivalents:
Match the following representations with their binary equivalents:
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Which of the following number systems has a base of 8?
Which of the following number systems has a base of 8?
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The binary number system uses the digits 0-1.
The binary number system uses the digits 0-1.
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What is the base of the hexadecimal number system?
What is the base of the hexadecimal number system?
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A number in a particular base is written as: (number)_______
A number in a particular base is written as: (number)_______
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Match the following number systems with their base:
Match the following number systems with their base:
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What is the decimal equivalent of the binary number (1101.01)2?
What is the decimal equivalent of the binary number (1101.01)2?
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In the decimal number system, the highest digit is 9.
In the decimal number system, the highest digit is 9.
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How do you convert a decimal integer to another base?
How do you convert a decimal integer to another base?
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What is the binary representation of (0.2345)10?
What is the binary representation of (0.2345)10?
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The octal value of (0.2345)10 is (0.17004)8.
The octal value of (0.2345)10 is (0.17004)8.
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What is the hexadecimal representation of (0.2345)10?
What is the hexadecimal representation of (0.2345)10?
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(0.625)10 converted to hexadecimal is _____ .
(0.625)10 converted to hexadecimal is _____ .
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Match the decimal numbers with their correct conversions:
Match the decimal numbers with their correct conversions:
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What base is used when converting decimal fractions to octal?
What base is used when converting decimal fractions to octal?
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A binary number can easily be converted to octal using a shortcut method.
A binary number can easily be converted to octal using a shortcut method.
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What is the purpose of the conversion process shown in the content?
What is the purpose of the conversion process shown in the content?
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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
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To convert a decimal integer to another base, perform successive integer divisions by the base of the new system.
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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.
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To convert decimal fractions, repeatedly multiply by the new base and record the integer part.
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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.
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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.
