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Questions and Answers
Which base represents the binary number system?
Which base represents the binary number system?
The octal number system uses the symbols 0 to 7.
The octal number system uses the symbols 0 to 7.
True
What is the value of the hexadecimal number 'A' in decimal?
What is the value of the hexadecimal number 'A' in decimal?
10
A collection of 8 bits is called a ______.
A collection of 8 bits is called a ______.
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Match the number systems with their base:
Match the number systems with their base:
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Which number system is primarily used by humans?
Which number system is primarily used by humans?
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The hexadecimal number system uses symbols beyond 0 to 9.
The hexadecimal number system uses symbols beyond 0 to 9.
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What two fundamental digits are used in the binary number system?
What two fundamental digits are used in the binary number system?
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What is the decimal equivalent of the binary number 101011₂?
What is the decimal equivalent of the binary number 101011₂?
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The weight for the binary bit furthest to the left is always zero.
The weight for the binary bit furthest to the left is always zero.
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What is the method used to convert octal numbers to decimal?
What is the method used to convert octal numbers to decimal?
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To convert hexadecimal to decimal, multiply each bit by ____ raised to the power of its weight.
To convert hexadecimal to decimal, multiply each bit by ____ raised to the power of its weight.
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Match the number system to its base:
Match the number system to its base:
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Which of the following best describes the process of converting decimal to binary?
Which of the following best describes the process of converting decimal to binary?
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The octal number 724₈ converts to 468₁₀ in decimal.
The octal number 724₈ converts to 468₁₀ in decimal.
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Calculate the decimal value of the hexadecimal number ABC₁₆.
Calculate the decimal value of the hexadecimal number ABC₁₆.
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What is the binary representation of the decimal number 117?
What is the binary representation of the decimal number 117?
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What is the octal equivalent of the decimal number 1234?
What is the octal equivalent of the decimal number 1234?
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The 10’s complement of 3675 is 6324.
The 10’s complement of 3675 is 6324.
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The binary equivalent of the octal number 705 is 111000101.
The binary equivalent of the octal number 705 is 111000101.
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If the value of 'k' in base 2 is 1024, what does it represent in terms of memory?
If the value of 'k' in base 2 is 1024, what does it represent in terms of memory?
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The ____’s complement of a number is obtained by subtracting the number from the power of the base.
The ____’s complement of a number is obtained by subtracting the number from the power of the base.
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What is the hexadecimal equivalent of the decimal number 1234?
What is the hexadecimal equivalent of the decimal number 1234?
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The binary representation of the hexadecimal number 10AF is ___
The binary representation of the hexadecimal number 10AF is ___
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Match the following prefixes with their values:
Match the following prefixes with their values:
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What does the symbol 'M' represent in computing?
What does the symbol 'M' represent in computing?
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Match the following conversion techniques with their descriptions:
Match the following conversion techniques with their descriptions:
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What is the octal equivalent of the binary number 10101111?
What is the octal equivalent of the binary number 10101111?
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The complement of a number is always a positive value.
The complement of a number is always a positive value.
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To convert a binary number to hexadecimal, you group bits in fours.
To convert a binary number to hexadecimal, you group bits in fours.
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What is the formula for calculating r’s complement?
What is the formula for calculating r’s complement?
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What is the octal equivalent of the binary number 110110?
What is the octal equivalent of the binary number 110110?
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The hexadecimal number 1F0C is equivalent to the octal number ___
The hexadecimal number 1F0C is equivalent to the octal number ___
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The result of converting the decimal number 33 to binary is:
The result of converting the decimal number 33 to binary is:
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What is the first step in finding the (r-1)'s complement using the shortcut method?
What is the first step in finding the (r-1)'s complement using the shortcut method?
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The binary 1's complement requires you to leave the digits unchanged until the first 1 is encountered.
The binary 1's complement requires you to leave the digits unchanged until the first 1 is encountered.
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Calculate the 10's complement of (529400)10.
Calculate the 10's complement of (529400)10.
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(A4D7E0)16 gives r's complement of ______ when calculated.
(A4D7E0)16 gives r's complement of ______ when calculated.
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Match the numbers with their corresponding r's complements:
Match the numbers with their corresponding r's complements:
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Study Notes
Introduction to Number Systems
- Base denotes the fundamental symbols in a numbering system (e.g., 0, 1, 2).
- Common numbering systems include:
- Decimal (Base 10)
- Binary (Base 2)
- Octal (Base 8)
- Hexadecimal (Base 16)
Common Number Systems
- Decimal (Base 10): Used by humans, symbols 0-9, not used by computers.
- Binary (Base 2): Symbols 0, 1; used by computers, not by humans.
- Octal (Base 8): Symbols 0-7; not used commonly, useful for representing long binary numbers.
- Hexadecimal (Base 16): Symbols 0-9, A-F; also useful for representing long binary numbers.
Counting in Different Bases
- Values of decimal, binary, octal, and hexadecimal representations are established.
- Example conversions show a range from 0 to 20.
Bits and Bytes
- A bit is the smallest unit in binary, while a byte is a collection of 8 bits.
- Binary system consists of two digits: 0 and 1.
Conversion Among Bases
- Techniques for converting between decimal, binary, octal, and hexadecimal systems are highlighted.
- For decimal representation, the weight or position of the digit affects its value exponentially based on the base.
Binary to Decimal Conversion
- Multiply each bit by 2 raised to the bit's position (weight).
- Sum all values to get the decimal equivalent.
Octal to Decimal Conversion
- Multiply each octal digit by 8 raised to its position.
- Add the results for the decimal output.
Hexadecimal to Decimal Conversion
- Multiply each hexadecimal digit by 16 raised to its position.
- Sum the products to convert into decimal.
Decimal to Binary Conversion
- Divide the decimal number by 2, recording remainders.
- The sequence of remainders gives the binary representation.
Decimal to Octal Conversion
- Divide the decimal number by 8, keeping track of remainders.
- The remainders will form the octal output.
Decimal to Hexadecimal Conversion
- Divide the decimal number by 16 and track the remainders.
- The sequence will give the hexadecimal representation.
Octal to Binary Conversion
- Convert each octal digit into its 3-bit binary equivalent.
Binary to Octal Conversion
- Group binary digits in sets of three, converting each group to an octal digit.
Hexadecimal to Binary Conversion
- Convert each hexadecimal digit to its 4-bit binary equivalent.
Binary to Hexadecimal Conversion
- Group bits in sets of four and convert each group to a single hexadecimal digit.
Octal to Hexadecimal and Vice Versa
- Use binary as a bridge for conversion between octal and hexadecimal formats.
Common Powers of 10 and 2
- Base 10 prefixes include pico, nano, micro, milli, kilo, mega, giga, and tera with respective values.
- Base 2 prefixes like kilo, mega, and giga have specific values relevant in computing.
Complement
- The complement of a number provides its negative equivalent.
- Two types of complements exist for a base: r's complement and (r-1)'s complement.
Finding r’s and (r-1)’s Complements
- r’s complement of a number is found using the formula r^n - N.
- (r-1)’s complement is calculated as r^n - N - 1.
- Shortcuts exist for finding complements, simplifying the process, especially in binary.
Examples of Complement Calculations
- Various examples illustrate how to compute complements in different bases using both the standard method and shortcuts, demonstrating practical applications.
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Description
This quiz covers the basics of numbering systems as introduced in Lecture 01 of CSE115: Computing Concepts. Students will explore different bases, including binary, octal, and hexadecimal, along with their significance and applications in computing.
