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Questions and Answers
What is the binary representation of the decimal number 10?
What is the binary representation of the decimal number 10?
Which base is used in the hexadecimal number system?
Which base is used in the hexadecimal number system?
Which of the following symbols is NOT used in the octal number system?
Which of the following symbols is NOT used in the octal number system?
What is the octal equivalent of the decimal number 16?
What is the octal equivalent of the decimal number 16?
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Which number system is primarily used by computers?
Which number system is primarily used by computers?
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How is the binary number 1010112 converted to decimal?
How is the binary number 1010112 converted to decimal?
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What is the decimal equivalent of the hexadecimal number ABC16?
What is the decimal equivalent of the hexadecimal number ABC16?
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Which technique is used for converting decimal numbers to binary?
Which technique is used for converting decimal numbers to binary?
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In binary to decimal conversion, what does the rightmost bit represent?
In binary to decimal conversion, what does the rightmost bit represent?
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To convert octal to decimal, which multiplication base is used?
To convert octal to decimal, which multiplication base is used?
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What is the first step in decimal to binary conversion?
What is the first step in decimal to binary conversion?
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In the conversion of 2510 to hexadecimal, what is the correct hexadecimal representation?
In the conversion of 2510 to hexadecimal, what is the correct hexadecimal representation?
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What is the binary representation of the hexadecimal number 10AF16?
What is the binary representation of the hexadecimal number 10AF16?
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Which step is NOT part of converting a decimal number to hexadecimal?
Which step is NOT part of converting a decimal number to hexadecimal?
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When converting binary 10101110112 to hexadecimal, what is the result?
When converting binary 10101110112 to hexadecimal, what is the result?
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What is the octal representation of the decimal number 1234?
What is the octal representation of the decimal number 1234?
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Which of the following represents the correct power and corresponding preface for $10^{-9}$?
Which of the following represents the correct power and corresponding preface for $10^{-9}$?
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Which of the following statements accurately describes the base-2 interpretation of 'mega' in memory computing?
Which of the following statements accurately describes the base-2 interpretation of 'mega' in memory computing?
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What is the correct conversion of 12510 to binary?
What is the correct conversion of 12510 to binary?
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Study Notes
Number Systems
- Common number systems include Decimal, Binary, Octal, and Hexadecimal.
- Decimal uses symbols 0-9, and is used by humans.
- Binary uses symbols 0 and 1, and is used by computers.
- Octal uses symbols 0-7.
- Hexadecimal uses symbols 0-9 and A-F.
Decimal, Binary, Octal, and Hexadecimal Conversion
- Tables show the conversion of numbers from decimal to binary, octal, and hexadecimal.
- For example, decimal 7 converts to binary 111, octal 7, and hexadecimal 7.
- Decimal 10 converts to binary 1010, octal 12, and hexadecimal A.
- Specific examples illustrate the translation process, such as 2510 = 110012 = 1916.
Conversion Techniques
- Methods for converting between number systems using various techniques.
- Decimal to binary involves repeated division by 2, retaining the remainders, (e.g. 12510 = 11111012).
- Hexadecimal to binary involves converting each hexadecimal digit to a 4-bit binary equivalent. (e.g. 10AF16 = 00010000101011112)
- Decimal to hexadecimal involves repeated division by 16, retaining remainders. The remainders are converted to hexadecimal digits based on the table.
Powers and Weights
- Conversion techniques involve understanding positional weights.
- Converting decimal 125 to its base-10 representation:
- 5 x 100 = 5
- 2 x 101 = 20
- 1 x 102 = 100
- Summing these gives 125
Binary Addition and Multiplication
- Addition and Multiplication operations are similar to those in decimal system, but instead with binary digits only.
Fractional Representation
- Decimal fractions can be converted into binary fractions using appropriate conversion steps.
- Binary fractions can also be converted into decimal numbers.
Common Powers of 10 and 2
- Various powers of 10 and their corresponding prefixes and symbols are described.
- Powers of 2 and their corresponding prefixes and values are described (e.g. 210 = 1024 = 1 Kilo).
- Examples demonstrate how computers use these units to represent memory capacity.
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Description
Explore the various number systems including Decimal, Binary, Octal, and Hexadecimal. Learn the techniques for converting numbers between these systems with practical examples. This quiz will help reinforce your understanding of how these systems operate and their applications.
