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Questions and Answers
What is the equivalent of decimal 15 in hexadecimal?
What is the equivalent of decimal 15 in hexadecimal?
Which number is represented as '1010' in decimal?
Which number is represented as '1010' in decimal?
In which number system is the symbol '1' used exclusively?
In which number system is the symbol '1' used exclusively?
Which of the following numbers is represented as '1101' in decimal?
Which of the following numbers is represented as '1101' in decimal?
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What is the base of the hexadecimal number system?
What is the base of the hexadecimal number system?
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What is the binary representation of the octal number 7058?
What is the binary representation of the octal number 7058?
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How would you convert the decimal number 123410 to octal?
How would you convert the decimal number 123410 to octal?
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What is the binary representation for the hexadecimal number 10AF16?
What is the binary representation for the hexadecimal number 10AF16?
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To convert from binary to octal, how do you group the bits?
To convert from binary to octal, how do you group the bits?
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Which of the following correctly converts the binary number 10101110112 to hexadecimal?
Which of the following correctly converts the binary number 10101110112 to hexadecimal?
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What is the output when converting the decimal number 123410 to hexadecimal?
What is the output when converting the decimal number 123410 to hexadecimal?
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How would you convert an octal number directly to hexadecimal?
How would you convert an octal number directly to hexadecimal?
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When converting the hexadecimal number 1F0C16 to octal, which method is used?
When converting the hexadecimal number 1F0C16 to octal, which method is used?
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What is the decimal equivalent of the binary number 101011?
What is the decimal equivalent of the binary number 101011?
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How do you convert the octal number 724 to decimal?
How do you convert the octal number 724 to decimal?
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What is the first step in converting a decimal number to binary?
What is the first step in converting a decimal number to binary?
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What is the hexadecimal equivalent of the decimal number 2748?
What is the hexadecimal equivalent of the decimal number 2748?
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Which of the following correctly describes the position of the bits when converting binary to decimal?
Which of the following correctly describes the position of the bits when converting binary to decimal?
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To convert the hexadecimal number ABC to decimal, which calculations should be performed?
To convert the hexadecimal number ABC to decimal, which calculations should be performed?
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What method is used when converting octal numbers to decimal?
What method is used when converting octal numbers to decimal?
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When converting a binary number like 1100 to decimal, which bit contributes to the highest value?
When converting a binary number like 1100 to decimal, which bit contributes to the highest value?
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What is the decimal equivalent of the binary number '1110101'?
What is the decimal equivalent of the binary number '1110101'?
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In computing, what is the value of the prefix 'M' in base 2?
In computing, what is the value of the prefix 'M' in base 2?
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Which of the following correctly lists the decimal equivalent of the hexadecimal number '1AF'?
Which of the following correctly lists the decimal equivalent of the hexadecimal number '1AF'?
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What is the result of adding the binary numbers '10101' and '11001'?
What is the result of adding the binary numbers '10101' and '11001'?
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What is the equivalent octal representation of the decimal number 33?
What is the equivalent octal representation of the decimal number 33?
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What does the prefix 'p' represent in the metric system?
What does the prefix 'p' represent in the metric system?
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Which of the following is the correct binary representation of the decimal number 75?
Which of the following is the correct binary representation of the decimal number 75?
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In the context of common powers, what is 10^6 commonly known as?
In the context of common powers, what is 10^6 commonly known as?
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Study Notes
Number Systems
- Common number systems: decimal, binary, octal, hexadecimal
- Decimal: base 10, uses symbols 0-9
- Binary: base 2, uses symbols 0 and 1, used in computers
- Octal: base 8, uses symbols 0-7
- Hexadecimal: base 16, uses symbols 0-9 and A-F
Quantities and Counting
- Numbers can be represented in different number systems
- Example: The decimal number 10 is equal to 1010 in binary, 12 in octal and A in hexadecimal
Conversion Between Number Systems
- Decimal to Decimal: Just for fun, no conversion needed
- Decimal to Binary: Divide by 2 repeatedly, keep track of remainders
- Decimal to Octal: Divide by 8 repeatedly, keep track of remainders
- Decimal to Hexadecimal: Divide by 16 repeatedly, keep track of remainders
- Binary to Decimal: Multiply each bit by 2^n, where n is the bit position starting from 0 on the right
- Octal to Decimal: Multiply each bit by 8^n, where n is the bit position starting from 0 on the right
- Hexadecimal to Decimal: Multiply each bit by 16^n, where n is the bit position starting from 0 on the right
- Binary to Octal: Group bits in threes, starting from the right, convert to octal digits
- Binary to Hexadecimal: Group bits in fours, starting from the right, convert to hexadecimal digits
- Octal to Binary: Convert each octal digit to a 3-bit binary representation
- Hexadecimal to Binary: Convert each hexadecimal digit to a 4-bit binary representation
- Octal to Hexadecimal: Use binary as an intermediary
- Hexadecimal to Octal: Use binary as an intermediary
Common Powers
-
Base 10:
- pico (p) = 10^-12
- nano (n) = 10^-9
- micro (µ) = 10^-6
- milli (m) = 10^-3
- kilo (k) = 10^3
- mega (M) = 10^6
- giga (G) = 10^9
- tera (T) = 10^12
-
Base 2: (used in computing, particularly for memory)
- kilo (k) = 2^10 = 1024
- mega (M) = 2^20 = 1,048,576
- giga (G) = 2^30 = 1,073,741,824
Binary Addition
- Adding two 1-bit values:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (carry over the "1")
- Adding two n-bit values:
- Add individual bits
- Propagate carries
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Description
Test your knowledge of different number systems including decimal, binary, octal, and hexadecimal. This quiz covers the representation of numbers and the methods for converting between these systems. Challenge yourself with conversions and see how well you understand the structure of numbers.
