Podcast
Questions and Answers
What is the base of the hexadecimal number system?
What is the base of the hexadecimal number system?
- 2
- 10
- 16 (correct)
- 8
The decimal number system is used by computers for internal representation.
The decimal number system is used by computers for internal representation.
False (B)
What is the process of converting a number from one number system to another?
What is the process of converting a number from one number system to another?
Conversion
The value of each digit in a number system is determined by its _______________________ and base.
The value of each digit in a number system is determined by its _______________________ and base.
Which of the following number systems uses digits 0-7?
Which of the following number systems uses digits 0-7?
Match the following number systems with their descriptions:
Match the following number systems with their descriptions:
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Study Notes
Number Systems Overview
A number system is a way to represent numbers using digits or symbols in a specific base or radix.
Types of Number Systems
- Decimal Number System (Base 10)
- Uses digits 0-9 to represent numbers
- Most commonly used number system
- Binary Number System (Base 2)
- Uses digits 0 and 1 to represent numbers
- Used by computers for internal representation
- Octal Number System (Base 8)
- Uses digits 0-7 to represent numbers
- Used in some computer programming
- Hexadecimal Number System (Base 16)
- Uses digits 0-9 and letters A-F to represent numbers
- Used in computer programming and web development
Number System Conversion
- Conversion between number systems:
- Decimal to Binary: Divide by 2 and keep remainder
- Decimal to Octal: Divide by 8 and keep remainder
- Decimal to Hexadecimal: Divide by 16 and keep remainder
- Conversion rules:
- Each digit in the original number system corresponds to a specific value in the new number system
- Follow the place value system (ones, tens, hundreds, etc.) when converting
Properties of Number Systems
- Base (Radix): The number of unique digits used in the number system
- Place Value: The value of each digit based on its position in the number
- Weight: The value of each digit based on its position and base
Number Systems Overview
- A number system represents numbers using digits or symbols in a specific base or radix.
Types of Number Systems
- Decimal Number System (Base 10): • Uses digits 0-9 to represent numbers • Most commonly used number system
- Binary Number System (Base 2): • Uses digits 0 and 1 to represent numbers • Used by computers for internal representation
- Octal Number System (Base 8): • Uses digits 0-7 to represent numbers • Used in some computer programming
- Hexadecimal Number System (Base 16): • Uses digits 0-9 and letters A-F to represent numbers • Used in computer programming and web development
Number System Conversion
- Conversion between number systems involves dividing by the base of the new system and keeping the remainder.
- Decimal to Binary conversion: divide by 2 and keep remainder.
- Decimal to Octal conversion: divide by 8 and keep remainder.
- Decimal to Hexadecimal conversion: divide by 16 and keep remainder.
Properties of Number Systems
- Base (Radix): the number of unique digits used in the number system.
- Place Value: the value of each digit based on its position in the number.
- Weight: the value of each digit based on its position and base.
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