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Questions and Answers
What digits are used in the Hexadecimal number system?
What digits are used in the Hexadecimal number system?
Which of the following represents the decimal number 11 in binary?
Which of the following represents the decimal number 11 in binary?
What is the first step in converting the decimal number 45 to binary?
What is the first step in converting the decimal number 45 to binary?
Which of the following correctly shows the addition of 1101 and 1011 in binary?
Which of the following correctly shows the addition of 1101 and 1011 in binary?
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How do you convert a binary number to octal?
How do you convert a binary number to octal?
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What is the base value for the Octal number system?
What is the base value for the Octal number system?
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In a place value system, if a digit's face value is 3 and it is in the tens place of base 10, what is its value?
In a place value system, if a digit's face value is 3 and it is in the tens place of base 10, what is its value?
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What is the result of the binary subtraction 1011 - 110?
What is the result of the binary subtraction 1011 - 110?
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Study Notes
Number Bases
- A number base is a system for representing numbers using a specific set of digits and place values.
- It defines the number of unique digits, including zero, used in a given numbering system.
- Base 10 (decimal) uses digits 0-9.
- Base 2 (binary) uses digits 0 and 1.
- Base 8 (octal) uses digits 0-7.
- Base 16 (hexadecimal) uses digits 0-9 and A-F.
Place Value System
- In any base system, the value of a digit depends on its face value (the actual digit) and its place value, which is a power of the base.
- For example, in base 10, the number 345 represents (3 x 102) + (4 x 101) + (5 x 100) = 345.
Converting Between Number Bases
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(i) Base 10 to Other Bases*
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To convert from base 10 to another base, successively divide the number by the new base and record the remainders.
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Continue dividing the quotients until the quotient is zero.
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Arrange the remainders in reverse order to obtain the representation in the new base.
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Example: Converting 45 (base 10) to base 2 yields 101101 (base 2).
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(ii) Other Bases to Base 10*
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To convert from another base to base 10, express each digit in the other base as a product of the digit and the corresponding power of the other base.
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Sum the products to get the base 10 equivalent.
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Example: 1011 (base 2) = (1 x 23) + (0 x 22) + (1 x 21) + (1 x 20) = 8 + 0 + 2 + 1 = 11 (base 10).
Arithmetic Operations in Number Bases
- Arithmetic operations (addition, subtraction) can be performed on numbers in different bases.
- Follow the rules of addition and subtraction, keeping in mind the place values. Note potential cases of carrying over values.
- Example: Adding 1102 and 1012 would be 10112.
Applications of Number Bases
- Used in computer systems, digital circuits, and measurements.
- Binary (base 2) is the fundamental language of computers, used to process data.
- Octal (base 8) and hexadecimal (base 16) are often used to simplify the representation of binary data.
- Time and angles are sometimes measured in base 60.
Conversion Tricks
- Binary to octal: Group digits in threes, starting from the right.
- Binary to hexadecimal: Group digits in fours, starting from the right.
- Octal/hexadecimal to binary: Expand each digit into its corresponding binary form.
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Description
This quiz explores various number bases, including decimal, binary, octal, and hexadecimal systems. It delves into the place value concept and provides methods for converting between different number bases. Test your knowledge on how digits represent values across multiple numbering systems.
