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Questions and Answers
What does the term 'digital' refer to?
What does the term 'digital' refer to?
A process that is achieved by using discrete units.
What is the radix or base of a number system?
What is the radix or base of a number system?
The number of different digits which can occur in each position in the number system.
What divides the integer and fractional parts in a positional number system?
What divides the integer and fractional parts in a positional number system?
Radix point.
How can a number in a base 'r' be generally written?
How can a number in a base 'r' be generally written?
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Which of the following are types of number systems? (Select all that apply)
Which of the following are types of number systems? (Select all that apply)
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How many unique symbols does the decimal number system contain?
How many unique symbols does the decimal number system contain?
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What symbols are used in the binary number system?
What symbols are used in the binary number system?
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What is the base or radix of the octal number system?
What is the base or radix of the octal number system?
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What symbols does the hexadecimal number system use?
What symbols does the hexadecimal number system use?
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What is the result of converting (10101)2 to decimal?
What is the result of converting (10101)2 to decimal?
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What is the result of converting (111.101)2 to decimal?
What is the result of converting (111.101)2 to decimal?
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In a binary to octal conversion, how are binary numbers grouped?
In a binary to octal conversion, how are binary numbers grouped?
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What is the octal equivalent of the binary number (101111010110.110110011)?
What is the octal equivalent of the binary number (101111010110.110110011)?
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Study Notes
Number Systems
- Digital processes use discrete units, each with an absolute and place value.
- Radix/Base determines the number of unique digits within a number system, and the value of each digit depends on its position.
- The Radix Point, similar to a decimal point, separates the integer and fractional portions of a number.
Types of Number Systems
- Decimal System uses ten digits (0-9) with a radix of 10. The value of a digit is calculated by multiplying it with the corresponding power of 10.
- Binary System is a base-2 system, using only 0 and 1. Each digit is multiplied by its corresponding power of 2. A binary digit is known as a bit.
- Octal System has a base of 8, using digits 0-7. It's related to binary, where every 3-bit group can be represented by an octal digit.
- Hexadecimal System is base-16, using digits 0-9 and letters A-F to represent values 10-15. Every 4-bit group of binary can be represented by a hexadecimal digit.
Conversions
- Binary to Decimal: Multiply each binary digit with its power of 2 and sum the results.
- Binary to Octal: Group binary digits into sets of three (starting from the binary point), convert each set to an octal digit.
- Binary to Hexadecimal: Group binary digits into sets of four, convert each set to a hexadecimal digit.
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Description
Explore the various number systems including decimal, binary, octal, and hexadecimal. Understand the significance of radix/base and how the radix point functions in these systems. Test your knowledge of the unique properties and conversion methods between these number systems.
