Numbering Systems Quiz

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Questions and Answers

Which of these numbering systems is used by computers to process information?

  • Octal
  • Decimal
  • Hexadecimal
  • Binary (correct)

What is the primary advantage of digital computers over other means of computation?

  • Speed and accuracy (correct)
  • Versatility
  • Cost-effectiveness
  • Ease of use

What is the role of numbering systems in aviation?

  • Improving flight safety by providing more accurate navigation data
  • Facilitating communication between pilots and air traffic controllers
  • Simplifying aircraft maintenance and troubleshooting
  • All of the above (correct)

Which number system is commonly referred to as 'hex'?

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

Which of the following is NOT a common application of computer systems in aviation?

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

What is the main reason why people and computers need methods of translating information?

<p>To overcome language barriers between humans and computers (D)</p> Signup and view all the answers

What is the primary purpose of converting numbers from one system to another?

<p>To facilitate information exchange between humans and computers (A)</p> Signup and view all the answers

What are the two states that a computer uses to represent data?

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

Which numbering system is used universally in everyday life?

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

How many possible values can be represented with 3 bits?

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

What is the term for a group of 4 bits?

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

What is the primary difference between analog and digital systems?

<p>Analog systems use continuous values, while digital systems use discrete values. (B)</p> Signup and view all the answers

What is the base of the binary number system?

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

What is the primary reason computers use binary instead of decimal?

<p>Binary is simpler to implement in hardware. (D)</p> Signup and view all the answers

What is the primary reason the Base 2 system is used by computers?

<p>It reflects the two states of transistors - ON or OFF. (C)</p> Signup and view all the answers

How does the zero impact the value of a number in positional notation?

<p>It represents a placeholder and indicates the absence of a particular digit in a specific position. (D)</p> Signup and view all the answers

Which of these is NOT a common numbering system besides decimal?

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

If a computer requires 10 different levels of brightness for a light, how many bits would it need?

<p>10 (C)</p> Signup and view all the answers

What is the significance of the position of a digit within a number?

<p>It defines the power of the base associated with each digit. (A)</p> Signup and view all the answers

Why is it easier to convert binary to octal or hexadecimal?

<p>They have a direct relationship with the number of bits used in binary. (B)</p> Signup and view all the answers

Which of the following is NOT a characteristic of the Base 10 system?

<p>Employs a base of 2 for representing values. (A)</p> Signup and view all the answers

In the Base 8 system, what is the value represented by the octal numeral 112?

<p>74 decimal (A)</p> Signup and view all the answers

What is the decimal equivalent of the binary number 1001010?

<p>74 (B)</p> Signup and view all the answers

What is the primary advantage of using hexadecimal over binary?

<p>Hexadecimal requires fewer digits to represent the same value as binary. (D)</p> Signup and view all the answers

Why is Base 2 system preferred for computers despite being less intuitive for humans?

<p>It is faster for computers to process. (A)</p> Signup and view all the answers

Which of the following accurately describes the relationship between octal and binary?

<p>Each octal digit represents 3 binary bits. (D)</p> Signup and view all the answers

When converting the octal number 362415 to decimal using the octal truth table, what is the value obtained for the digit '6'?

<p>98304 (D)</p> Signup and view all the answers

Using the binary to decimal truth table, what is the decimal equivalent of the binary number 10010112?

<p>75 (C)</p> Signup and view all the answers

In the division method for converting decimal numbers to binary, why is the remainder of each division important?

<p>The remainders represent the binary digits of the converted number. (A)</p> Signup and view all the answers

What is the primary difference between converting from octal to decimal versus directly converting from binary to decimal?

<p>Converting from octal first involves converting to binary before using the binary to decimal truth table. (A)</p> Signup and view all the answers

In the subtraction method for converting decimal to binary, what is the significance of the largest power of 2 that is less than the decimal number being converted?

<p>It represents the highest binary digit in the converted number. (B)</p> Signup and view all the answers

What is the hexadecimal equivalent of the decimal number 22?

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

What is the decimal equivalent of the hexadecimal number 100?

<p>256 (B)</p> Signup and view all the answers

What is the binary equivalent of the decimal number 17?

<p>10001 (B)</p> Signup and view all the answers

Which of the following statements accurately describes the relationship between hexadecimal and binary numbers?

<p>Each hexadecimal digit corresponds to four binary digits. (B)</p> Signup and view all the answers

Which of the following is the correct binary representation of the hexadecimal number 2A?

<p>0010 1010 (C)</p> Signup and view all the answers

Flashcards

Binary Number System

A numbering system that uses only two digits: 0 and 1.

Octal Number System

A numbering system that uses eight digits: 0 to 7.

Hexadecimal Number System

A numbering system that uses sixteen symbols: 0-9 and A-F.

Decimal to Binary Conversion

The process of converting a decimal number into its binary equivalent.

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Binary to Decimal Conversion

The process of changing a binary number into its decimal equivalent.

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Applications of Numbering Systems

Numbering systems are crucial in fields like aviation, military, and commercial functions.

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Decimal Number System

The standard numerical system that uses ten digits (0-9).

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Binary to Decimal Conversion Process

The method for converting binary numbers into decimal format through power of two calculations.

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Decimal to Binary Conversion by Division Method

A technique to convert decimal numbers into binary by repeatedly dividing by 2 and tracking remainders.

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Binary Number Representation of 75

The binary equivalent of the decimal number 75 is 1001011.

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Octal to Decimal Conversion Method

Converting octal numbers to decimal by first translating octal to binary, then binary to decimal.

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Subtraction Method for Binary Conversion

A conversion technique that uses subtraction to convert decimal numbers into binary format instead of division.

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Digital Values

Numerical values used in digital systems, as opposed to continuous values.

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Discreteness in Digital

Digital systems represent information using discrete values rather than continuous signals.

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Binary Digit (Bit)

The smallest unit of data in a computer, representing a state of on (1) or off (0).

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Nibble

A group of four bits, which can represent 16 different values.

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Value Representation in Computers

Computers use binary numbers to represent various states or conditions.

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Base 2 System

Another term for the binary number system, utilizing only 0 and 1.

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Base 8 (Octal)

A numbering system that uses eight symbols: 0-7 and is derived from binary.

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Base 16 (Hexadecimal)

A numbering system using sixteen symbols (0-9 and A-F), often used in computing.

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Conversion Process

The method of changing numbers between binary, octal, decimal, and hexadecimal formats.

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Digit Levels in Binary

The number of values that can be represented by a certain number of bits (e.g., 2^n).

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Hexadecimal Digits

Hexadecimal uses digits 0-9 and letters A-F to represent values.

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Decimal 16 in Hexadecimal

The decimal number 16 equals 10 in hexadecimal.

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Consecutive Hexadecimal Numbers

In hex, after 1F comes 20, indicating a new digit.

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Binary to Decimal Example 1

100012 in binary converts to 1710 in decimal.

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Binary to Decimal Example 2

110011012 in binary converts to 20510 in decimal.

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Hexadecimal Representation

Each hex digit represents four binary digits (bits).

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Base Annotation Importance

Using subscripts clarifies which numbering system is used.

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From FF to 100 in Hex

Hexadecimal FF equals decimal 255, followed by 100 in hex (256).

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Incrementing Hex Numbers

Change the second digit from F to 0 when incrementing.

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Hexadecimal Series Example

Hex series starts from 10 to 1F, 20 to 2F, etc.

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Positional Notation

A system where the position of a digit determines its value.

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Exponent

A number indicating how many times to multiply the base by itself.

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Base 10

The decimal system that uses ten digits, widely used in daily life.

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Base 2

The binary system that uses two digits: 0 and 1, fundamental in computing.

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Base 8

The octal system that uses eight digits (0-7), often used in computer applications.

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Base 16

The hexadecimal system that uses sixteen symbols (0-9 and A-F).

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Role of Zero

Zero's position is essential in determining the value of numbers.

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Binary to Octal

The process of converting binary digits into octal by grouping.

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Decimal Value Example

The value of 6348 is equivalent to 41210 in a specific base.

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Study Notes

Numbering Systems (5.2)

  • Learning Objectives:
    • Identify binary, octal, and hexadecimal numbering systems
    • Recall decimal-to-binary/octal/hexadecimal conversions
    • Recall binary/octal/hexadecimal-to-decimal conversions

Applications of Numbering Systems

  • Computers perform repeated calculations and data processing in various fields (aviation, military, scientific, commercial)
  • Digital computers offer speed, accuracy, and manpower savings, often automating tasks and freeing personnel for higher-level work

Numbering Systems

  • Common numbering systems include decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16)
  • Each system uses unique symbols/units and a base defining the values of positions within the system
  • Decimal system uses digits 0-9
  • Binary system uses digits 0 and 1
  • Octal system uses digits 0-7
  • Hexadecimal system uses digits 0-9 and A-F

Units and Numbers

  • Decimal system: unit is a single object, a number represents a quantity (e.g., 5 apples)
  • Units and quantities are represented using symbols known as Arabic numerals (0, 1, 2, …, 9)
  • Number systems use different symbols, including letters, for representing values (e.g., Roman numerals)

Numbering Systems - Base

  • Numbers are a combination of base, unit and number
  • Base refers to the number of unique symbols used in the system
  • The base defines the values of positions (e.g., in base 10, right-most is 100, next 101, etc.)
  • Highest value symbol in a system is always one less than the number base. -Base 10 = 0-9 -Base 2 = 0-1 -Base 8 = 0-7
  • Base 16 = 0-9 and A-F

Positional Notation and Zero

  • Positional notation determines a number's value by the symbol and its position within the numeral
  • Zero in a number system represents a space where a quantity is absent.

Digital Numbering Systems

  • Decimal (Base 10) is widely used for counting and recording general values
  • Binary (Base 2) is used in computers for calculations; represents 'on' or 'off' (1 or 0) states
  • Octal (Base 8) provides a compact representation of binary numbers through grouping of bits (3 binary bits = 1 octal digit)
  • Hexadecimal (Base 16) efficiently represents binary numbers using 4 binary bits or 1 hex digit; uses digits 0-9 & characters A-F

Converting Between Numbering Systems

  • Methods to convert decimal to binary/octal/hexadecimal and vice-versa include division, subtraction, truth tables, and positional notation.

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