Number Systems Quiz
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Questions and Answers

What is the binary representation of the decimal number 10?

The binary representation of the decimal number 10 is 1010.

Which number systems are utilized in computers?

The binary and hexadecimal number systems are used in computers.

Convert the decimal number 15 to its hexadecimal equivalent.

The hexadecimal equivalent of the decimal number 15 is F.

Identify the base of the octal number system and its symbols.

<p>The base of the octal number system is 8, using symbols <code>0</code> to <code>7</code>.</p> Signup and view all the answers

What is the relationship between the decimal number 25 and its binary equivalent?

<p>The decimal number 25 is equivalent to <code>11001</code> in binary.</p> Signup and view all the answers

In the context of number systems, what does the term 'base' refer to?

<p>The term 'base' refers to the number of unique digits, including zero, used to represent numbers in a system.</p> Signup and view all the answers

What is the octal representation of the decimal number 8?

<p>The octal representation of the decimal number 8 is <code>10</code>.</p> Signup and view all the answers

Convert the decimal number 117 into binary format.

<p>1110101</p> Signup and view all the answers

What does the prefix 'milli' represent in terms of power of ten?

<p>10⁻³ or 0.001</p> Signup and view all the answers

How do you convert the binary number 10101 to decimal?

<p>21</p> Signup and view all the answers

What is the decimal value of 2⁶ and its equivalent in kilobytes?

<p>64 and 64k</p> Signup and view all the answers

Demonstrate how to add the binary numbers 10101 and 11001.

<p>101110</p> Signup and view all the answers

How do you convert the decimal number 125 to binary?

<p>Divide 125 by 2 repeatedly, tracking the remainders, to get 1111101 in binary.</p> Signup and view all the answers

What is the binary representation of the decimal number 0.6875?

<p>The binary representation is 0.1011.</p> Signup and view all the answers

Explain the method to convert binary 101011 to decimal.

<p>Multiply each bit by 2 raised to its weight and sum the results, yielding 43 in decimal.</p> Signup and view all the answers

Describe how to convert the octal number 724 to decimal.

<p>Multiply each digit by 8 raised to its weight and sum the totals to get 468 in decimal.</p> Signup and view all the answers

What technique do you use to convert hexadecimal numbers to decimal?

<p>Multiply each digit by 16 raised to its position's weight and sum all the results.</p> Signup and view all the answers

How does the remainder play a role in converting decimal to binary?

<p>Each remainder indicates a bit value in the binary representation, starting from the least significant bit.</p> Signup and view all the answers

If 101001 in binary is converted to decimal, what is the value?

<p>The value is 41 in decimal.</p> Signup and view all the answers

What is the conversion of the decimal number 41.6875 into binary?

<p>The binary representation is 101001.1011.</p> Signup and view all the answers

Outline the process of converting a decimal fraction to binary.

<p>Multiply the fractional part by 2 and take the integer part iteratively until it reaches 0.</p> Signup and view all the answers

How do you convert a binary number to octal?

<p>Group the bits in threes starting from the right and convert each group to its octal equivalent.</p> Signup and view all the answers

What is the octal equivalent of the binary number $1011010111_2$?

<p>The octal equivalent is $1327_8$.</p> Signup and view all the answers

Describe the process of converting binary to hexadecimal.

<p>Group the bits in fours starting from the right and convert each group to its hexadecimal representation.</p> Signup and view all the answers

What is the hexadecimal equivalent of the binary number $1010111011_2$?

<p>The hexadecimal equivalent is $2BB_{16}$.</p> Signup and view all the answers

How can you convert an octal number to hexadecimal?

<p>Use binary as an intermediary by first converting octal to binary, then binary to hexadecimal.</p> Signup and view all the answers

What is the hexadecimal equivalent of the octal number $1076_8$?

<p>The hexadecimal equivalent is $23E_{16}$.</p> Signup and view all the answers

What is the purpose of grouping bits in threes when converting binary to octal?

<p>Grouping bits in threes aligns with the base-8 structure of the octal system.</p> Signup and view all the answers

Explain the role of binary when converting between octal and hexadecimal.

<p>Binary serves as an intermediary format that allows for straightforward conversion between the two bases.</p> Signup and view all the answers

What technique is used when converting a hexadecimal number to octal?

<p>Use binary as an intermediary by converting the hexadecimal digits to binary, then the resulting binary to octal.</p> Signup and view all the answers

What is the octal equivalent of the hexadecimal number $1F0C_{16}$?

<p>The octal equivalent is $17414_8$.</p> Signup and view all the answers

Convert the hexadecimal number $1C3_{16}$ to decimal. What is the result?

<p>The decimal equivalent of $1C3_{16}$ is $451_{10}$.</p> Signup and view all the answers

What is the binary equivalent of the octal number $527_8$?

<p>The binary equivalent of $527_8$ is $101010111_2$.</p> Signup and view all the answers

How would you convert the decimal number $2500_{10}$ to octal?

<p>The octal representation of $2500_{10}$ is $4750_8$.</p> Signup and view all the answers

What is the binary representation of the hexadecimal number $2B3_{16}$?

<p>The binary representation of $2B3_{16}$ is $001010110011_2$.</p> Signup and view all the answers

Convert the decimal fraction $0.875_{10}$ to octal.

<p>The octal representation of $0.875_{10}$ is $0.7_8$.</p> Signup and view all the answers

Find the decimal equivalent of the hexadecimal number $A5_{16}$.

<p>The decimal equivalent of $A5_{16}$ is $165_{10}$.</p> Signup and view all the answers

Convert the decimal number $453_{10}$ to hexadecimal.

<p>The hexadecimal representation of $453_{10}$ is $1C5_{16}$.</p> Signup and view all the answers

What is the binary form of the octal number $612_8$?

<p>The binary form of $612_8$ is $110001010_2$.</p> Signup and view all the answers

Convert the decimal number $0.625_{10}$ to octal. What is the result?

<p>The octal representation of $0.625_{10}$ is $0.5_8$.</p> Signup and view all the answers

Flashcards

Decimal Number System

A number system that uses 10 digits (0-9) and has a base of 10.

Binary Number System

A number system that uses only 2 digits (0 and 1) and has a base of 2.

Octal Number System

A number system that uses 8 digits (0-7) and has a base of 8.

Hexadecimal Number System

A number system that uses 16 digits (0-9 and A-F) and has a base of 16.

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Base of a Number System

The number of unique symbols used in a number system.

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Converting between number systems

The process of changing a number from one number system to another (e.g., decimal to binary).

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Example Conversion (25 decimal to binary)

25 in base-10 is equal to 11001 in base-2.

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Decimal to Binary Conversion

Converting a number from base 10 (decimal) to base 2 (binary).

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Binary to Decimal Conversion

Converting a number from base 2 (binary) to base 10 (decimal).

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Octal to Decimal Conversion

Converting a number from base 8 (octal) to base 10 (decimal).

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Hexadecimal to Decimal Conversion

Converting a number from base 16 (hexadecimal) to base 10 (decimal).

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Least Significant Bit (LSB)

The rightmost bit in a binary number.

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Decimal Fraction to Binary

Converting a decimal fraction to binary.

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Binary Addition: Carry Propagation

In adding two binary numbers, when the sum of two bits is '10', a carry bit is generated and added to the next digit position.

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What are 'k', 'M', and 'G' in computer memory?

In computer memory, 'k' represents kilobytes (2^10), 'M' represents megabytes (2^20), and 'G' represents gigabytes (2^30).

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Decimal to Octal Conversion

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

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Decimal to Hexadecimal Conversion

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

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Hexadecimal Digit to Binary

Each single hexadecimal digit can be represented with a 4-bit binary value.

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Octal Digit to Binary

Each single octal digit can be represented with a 3-bit binary value.

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Decimal Fraction to Octal

Converting a fractional decimal number to its octal equivalent, using successive multiplications with the base.

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Hexadecimal to Binary Conversion Process

Convert hexadecimal numbers to binary by converting each hexadecimal digit to its 4-bit binary equivalent.

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Octal to Binary Conversion Process

Converting octal digits (base 8) to binary (base 2).

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Base Conversion

The process of converting numbers from one base (like decimal, binary, octal, or hexadecimal) to another.

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Binary to Octal Conversion

Converting a binary number to its equivalent octal representation involves grouping the binary digits into sets of three, starting from the rightmost digit, and converting each group into its corresponding octal digit.

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Binary to Hexadecimal Conversion

This conversion involves grouping the binary digits into sets of four, starting from the rightmost digit, and then converting each group to its equivalent hexadecimal digit.

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Octal to Hexadecimal Conversion

Converting an octal number to hexadecimal requires an intermediate step of converting it to binary first, then grouping the binary digits in fours to arrive at the hexadecimal equivalent.

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Hexadecimal to Octal Conversion

This conversion uses binary as an intermediary. First, convert the hexadecimal number to binary, then group the binary digits into threes to obtain the octal equivalent.

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What are the symbols used in hexadecimal?

Hexadecimal uses the digits 0-9 and the letters A-F, representing values 10 through 15.

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How many bits are needed to represent one hexadecimal digit?

Four binary bits are required to represent a single hexadecimal digit.

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What is the base of the octal number system?

The base of the octal number system is 8, meaning it uses 8 unique digits (0-7).

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How many decimal places are there in the binary number system?

There are only two decimal places in the binary number system: 0 and 1.

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Study Notes

Number Systems

  • Various number systems exist, including Decimal, Binary, Octal, and Hexadecimal.
  • Decimal is used by humans, employing digits 0-9.
  • Binary uses only 0 and 1, fundamental in computer operation.
  • Octal uses digits 0-7.
  • Hexadecimal uses digits 0-9 and letters A-F.

Common Number Systems

  • Decimal (Base 10): Used by humans; symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; used by humans, not computers.
  • Binary (Base 2): Used by computers; symbols 0, 1; not used by humans.
  • Octal (Base 8): Used by computers; symbols 0, 1, 2, 3, 4, 5, 6, 7; not used by humans.
  • Hexadecimal (Base 16): Used by computers; symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F; not used by humans.

Quantities/Counting

  • Conversion tables showing decimal, binary, octal, and hexadecimal equivalents for numbers 0-7.

Conversion Among Bases

  • Decimal, binary, octal, and hexadecimal are interconnected; conversion between systems is possible.

Quick Example

  • 2510 = 110012 = 318 = 1916

Decimal to Binary Conversion

  • Technique: Divide the decimal number by 2 repeatedly; record the remainders.

Decimal to Binary Conversion (Example)

  • 12510 = 11111012

Decimal to Binary Conversion (Example, Fracional Part)

  • 0.687510 = 0.10112

Binary to Decimal Conversion

  • Technique: Multiply each bit by 2n, where n is the bit's position (starting from 0 on the right). Add the results.

Binary to Decimal Conversion (Example)

  • 1010112 = 4310

Octal to Decimal Conversion

  • Technique: Multiply each bit by 8n, where n is the bit's position (starting from 0 on the right). Sum the results.

Octal to Decimal Conversion (Example)

  • 7248 = 46810

Hexadecimal to Decimal Conversion

  • Technique: Multiply each bit by 16n, where n is the bit's position (starting from 0 on the right). Sum the results

Hexadecimal to Decimal Conversion (Example)

  • ABC16 = 274810

Octal to Binary Conversion

  • Technique: Convert each octal digit to its 3-bit binary equivalent

Octal to Binary Conversion (Example)

  • 7058 = 1110001012

Binary to Octal Conversion

  • Technique: Group binary digits in threes, starting from right, and convert each group to its octal equivalent

Binary to Hexadecimal Conversion

  • Technique: Group binary digits in fours, starting from the right, and convert each group to its hexadecimal equivalent.

Decimal to Octal Conversion

  • Technique: Divide the decimal number by 8; record the remainders.

Decimal to Hexadecimal Conversion

  • Technique: Divide the decimal number by 16; record the remainders.

Binary to Octal (Example)

  • 10110101112 = 13278

Binary to Hexadecimal (Example)

  • 10101110112 = 2BB16

Octal to Hexadecimal

  • Technique Use binary as an intermediate steps

Octal to Hexadecimal (Example)

  • 10768 = 23E16

Hexadecimal to Octal

  • Technique: Use binary as an intermediate step.

Hexadecimal to Octal (Example)

  • 1F0C16 = 174148

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Number System - Final 1 - PDF

Description

Test your knowledge on various number systems including Decimal, Binary, Octal, and Hexadecimal. This quiz will cover their definitions, uses, and conversion methods among these bases. Challenge yourself and see how well you understand these fundamental concepts in mathematics and computer science.

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