Number Systems and Conversions

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Questions and Answers

What is the binary representation of the decimal number 10?

  • 1001
  • 1010 (correct)
  • 1100
  • 1110

Which base is used in the hexadecimal number system?

  • 16 (correct)
  • 8
  • 10
  • 2

Which of the following symbols is NOT used in the octal number system?

  • 8 (correct)
  • 6
  • 3
  • 1

What is the octal equivalent of the decimal number 16?

<p>20 (D)</p> Signup and view all the answers

Which number system is primarily used by computers?

<p>Binary (B)</p> Signup and view all the answers

How is the binary number 1010112 converted to decimal?

<p>43 (A)</p> Signup and view all the answers

What is the decimal equivalent of the hexadecimal number ABC16?

<p>2748 (B)</p> Signup and view all the answers

Which technique is used for converting decimal numbers to binary?

<p>Dividing by two and tracking remainders (B)</p> Signup and view all the answers

In binary to decimal conversion, what does the rightmost bit represent?

<p>1 (B)</p> Signup and view all the answers

To convert octal to decimal, which multiplication base is used?

<p>8 (A)</p> Signup and view all the answers

What is the first step in decimal to binary conversion?

<p>Divide by two (B)</p> Signup and view all the answers

In the conversion of 2510 to hexadecimal, what is the correct hexadecimal representation?

<p>19 (C)</p> Signup and view all the answers

What is the binary representation of the hexadecimal number 10AF16?

<p>0001000010101111 (B)</p> Signup and view all the answers

Which step is NOT part of converting a decimal number to hexadecimal?

<p>Convert remainders to binary. (C)</p> Signup and view all the answers

When converting binary 10101110112 to hexadecimal, what is the result?

<p>2BB (B)</p> Signup and view all the answers

What is the octal representation of the decimal number 1234?

<p>2342 (B)</p> Signup and view all the answers

Which of the following represents the correct power and corresponding preface for $10^{-9}$?

<p>n - nano (C)</p> Signup and view all the answers

Which of the following statements accurately describes the base-2 interpretation of 'mega' in memory computing?

<p>1 mega equals 1,048,576 bytes. (A)</p> Signup and view all the answers

What is the correct conversion of 12510 to binary?

<p>11111001 (A)</p> Signup and view all the answers

Flashcards

Binary Number System

A number system with a base of 2, using only the digits 0 and 1.

Octal Number System

A number system with a base of 8, using digits from 0 to 7.

Hexadecimal Number System

A number system with a base of 16, using digits from 0 to 9 and letters A to F.

Place Value in Number Systems

Numbers are represented by a sequence of digits, where each digit's place value is a power of the base.

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Number System Conversion

Converting between number systems involves expressing a value in one system using the equivalent representation in another system.

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Converting Binary or Hexadecimal to Decimal

The process of calculating a number's value in the decimal system, starting from binary or hexadecimal.

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Binary to Decimal Conversion

The sum of the products of each binary digit (0 or 1) and its corresponding weight, which is a power of 2.

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Hexadecimal to Decimal Conversion

The sum of the products of each hexadecimal digit (0-9, A-F) and its corresponding weight, which is a power of 16.

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Decimal to Binary Conversion

The process of converting a decimal number to its binary representation. It involves repeatedly dividing the decimal number by 2 and recording the remainders, forming the bits.

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Binary Number

A representation of a number using only the digits 0 and 1, with each digit's place value being a power of 2.

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Decimal Number System (Base 10)

A base-10 number system, where each digit's weight is a power of 10.

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Hexadecimal to Binary Conversion

A technique for converting a number from hexadecimal to binary by representing each hex digit as its 4-bit binary equivalent.

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Binary Number System (Base 2)

A base-2 number system using only two digits (0 and 1), where each digit's weight is a power of 2.

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Decimal to Hexadecimal Conversion

A technique for converting a decimal number to hexadecimal by repeatedly dividing by 16 and keeping track of the remainders.

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Binary to Hexadecimal Conversion

A technique for converting a binary number to hexadecimal by grouping the bits into sets of four, starting from the rightmost bit, and then converting each group to its hexadecimal equivalent.

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Hexadecimal Number System (Base 16)

A base-16 number system, using digits 0-9 and letters A-F, where each digit's weight is a power of 16.

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Common Powers of 10

Powers of 10, used to represent very large or very small numbers in a more concise way.

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Common Powers of 2 in Computing

Powers of 2 that are commonly used in computing, particularly for memory sizes.

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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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Related Documents

Lecture 1 Number System PDF

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