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Questions and Answers
What is the binary representation of the decimal number 25?
The octal representation of the decimal number 25 is (32)8.
False
What is the hexadecimal representation of the decimal number 25?
(19)16
A decimal fraction is converted to any other base by using multiplication by the ______.
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Match the following decimal numbers with their equivalent representations in binary, octal, and hexadecimal:
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What is the binary representation of (0.2345)10?
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(0.2345)10 is equal to (0.17004)8 in octal.
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What is the process of converting a decimal fraction to binary called?
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The hexadecimal equivalent of (0.2345)10 is (0.______)16.
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What is the base of the Decimal Number System?
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Match the decimal fractions with their correct binary equivalents:
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The Octal Number System has a base of 16.
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Which of the following is the correct base for the octal number system?
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What is the decimal representation of (456.41)8?
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In the conversion to hexadecimal, the digit 'A' represents 10.
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What is the binary of the decimal number 234.625?
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In the Binary Number System, the base is ______.
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Match the following number systems with their bases:
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Which of the following calculations represents (1FA.4C)16 in Decimal?
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(1101.01)2 equals 13.25 in Decimal.
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How do you convert a Decimal integer to another base?
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Study Notes
Introduction to Computer Systems: Data Representation
- Data comes in various forms: numbers, text, audio, images, video, and multimedia (combinations of these).
- All data types must be represented as 0s and 1s for computer storage and processing.
- Encoding is the method of representing data as 0s and 1s.
Number Systems
- Number systems (bases, or radices) use unique symbols (digits) to represent numbers.
- Digits have both a value and a positional value (based on its position). A number in a specific base is written as (number)base.
- Decimal (base 10) uses digits 0-9. A number like 5432 in base 10 can be calculated as 5 * 10^3 + 4 * 10^2 + 3 * 10^1 + 2 * 10^0 = 5432.
- Common number systems (bases) include binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16).
- Binary uses 0 and 1, Octal uses 0-7, Decimal uses 0-9 and Hexadecimal uses 0-9 and A-F.
- The number of possible values in N digits in base R is RN
Converting Decimal to Other Bases
- Integer conversion: Use integer division by the new base to find remainders.
- Fractional conversion: Multiply the decimal by the new base, retain the integer portion of the product, which becomes the next digit, and repeat.
Converting Between Binary, Octal, and Hexadecimal
- Shortcut methods exist for converting between these bases.
- Octal conversion uses groups of 3 binary digits.
- Hexadecimal conversion uses groups of 4 binary digits.
Binary Arithmetic
- Binary addition, subtraction and other operations are performed using the rules of base-2 arithmetic.
- Key rules are readily available for addition and subtraction.
- Overflow happens when the result of a calculation exceeds the available bits, leading to incorrect representation and potentially incorrect results.
Floating-Point Representation
- Represents real numbers as mantissa x baseexponent.
- Mantissa: The significant digits.
- Exponent: The power to which the base is raised.
IEEE Standard 754
- Standard format for representing floating-point numbers in computers.
- Standardized for single and double precision representations.
- Specific bit layouts define the sign, exponent, and mantissa portions.
Character Coding Schemes
- Codes like ASCII and Unicode represent characters, digits, and symbols as specific bit patterns.
- Each character has a unique bit pattern.
- EBCDIC and ASCII are commonly encountered character coding schemes.
- Unicode is compatible with most other codes allowing text to be exchanged between systems that may use different character codes.
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Description
This quiz covers the fundamental concepts of data representation in computer systems, including the different types of data and their encoding as binary. It delves into various number systems, such as binary, octal, decimal, and hexadecimal, along with their respective conversions. Test your understanding of how numbers are represented and manipulated in computing.
