Questions and Answers
What is the base of the hexadecimal number system?
16
The decimal number system is used by computers for internal representation.
False
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.
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Which of the following number systems uses digits 0-7?
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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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Description
Learn about different number systems, including decimal, binary, and octal. Understand the base and digits used in each system.
