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Questions and Answers
What is the least significant bit (LSB) in the binary conversion of $125_{10}$?
What is the least significant bit (LSB) in the binary conversion of $125_{10}$?
The hexadecimal system is based on 10.
The hexadecimal system is based on 10.
False
What binary number does the decimal number $41.6875_{10}$ convert to?
What binary number does the decimal number $41.6875_{10}$ convert to?
101001.1011
To convert a decimal number to binary, you keep track of the ______ after dividing by two.
To convert a decimal number to binary, you keep track of the ______ after dividing by two.
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Match the following number systems to their base:
Match the following number systems to their base:
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What is the decimal equivalent of $ABC_{16}$?
What is the decimal equivalent of $ABC_{16}$?
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The binary representation of $705_8$ is $111000101_2$.
The binary representation of $705_8$ is $111000101_2$.
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What is the 3-bit binary equivalent for the octal digit 6?
What is the 3-bit binary equivalent for the octal digit 6?
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Which number system is primarily used in computers?
Which number system is primarily used in computers?
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To convert from decimal to octal, you must divide by ___ and keep track of the remainder.
To convert from decimal to octal, you must divide by ___ and keep track of the remainder.
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Match the following examples with their respective conversions:
Match the following examples with their respective conversions:
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The hexadecimal system uses the number 10 as a symbol.
The hexadecimal system uses the number 10 as a symbol.
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What is the base of the octal number system?
What is the base of the octal number system?
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In the decimal system, the highest single digit is ______.
In the decimal system, the highest single digit is ______.
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Match the following number systems with their respective bases:
Match the following number systems with their respective bases:
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Which symbols are used in the hexadecimal number system?
Which symbols are used in the hexadecimal number system?
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The octal system is used by humans for everyday counting.
The octal system is used by humans for everyday counting.
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What is the binary representation of the decimal number 5?
What is the binary representation of the decimal number 5?
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What is the octal representation of the binary number $1011010111_2$?
What is the octal representation of the binary number $1011010111_2$?
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$1076_8$ is equal to $23E_{16}$.
$1076_8$ is equal to $23E_{16}$.
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What is the hexadecimal representation of the binary number $1010111011_2$?
What is the hexadecimal representation of the binary number $1010111011_2$?
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The binary number $1F0C_{16}$ converts to octal as $______$.
The binary number $1F0C_{16}$ converts to octal as $______$.
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Match the binary numbers to their equivalent octal representations:
Match the binary numbers to their equivalent octal representations:
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What is the binary product of the values 1110 and 1011?
What is the binary product of the values 1110 and 1011?
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The decimal number 3.14579 converts to the binary representation 11.001001...
The decimal number 3.14579 converts to the binary representation 11.001001...
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What is the decimal equivalent of the binary number 10.1011?
What is the decimal equivalent of the binary number 10.1011?
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The binary number system is based on powers of ____.
The binary number system is based on powers of ____.
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Match the following decimal values with their respective binary representations:
Match the following decimal values with their respective binary representations:
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What is the hexadecimal representation for the decimal number 117?
What is the hexadecimal representation for the decimal number 117?
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The binary number for the decimal number 431 is 110101111.
The binary number for the decimal number 431 is 110101111.
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What is the value of the prefix 'm' in the base 10 system?
What is the value of the prefix 'm' in the base 10 system?
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In base 2, the value of G is __________.
In base 2, the value of G is __________.
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Match the following decimal numbers with their binary equivalents:
Match the following decimal numbers with their binary equivalents:
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What result is obtained when performing binary addition on A: 1101 and B: 1011?
What result is obtained when performing binary addition on A: 1101 and B: 1011?
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The value of pico (p) is equal to 10^-9.
The value of pico (p) is equal to 10^-9.
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How do you multiply two powers with the same base?
How do you multiply two powers with the same base?
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Study Notes
Number Systems
- Number systems are used to represent quantities in different bases.
- Common Number Systems:
- Decimal (Base 10): Uses symbols 0-9, used by humans.
- Binary (Base 2): Uses symbols 0 and 1, used by computers.
- Octal (Base 8): Uses symbols 0-7, used in some computing contexts.
- Hexadecimal (Base 16): Uses symbols 0-9 and A-F, used extensively due to its compact representation.
Conversion Between Bases
- Various methods exist to convert between number systems.
- Decimal to Binary: Repeated division by 2, retaining remainders to form the binary representation.
- Binary to Decimal: Multiply each bit by 2 raised to its respective position from right (0 for rightmost). Sum all the products.
- Decimal to Octal: Similar to Decimal to Binary, by dividing successively by 8.
- Octal to Decimal: Similar to Binary to Decimal, but each octal digit is multiplied by 8 raised to its position.
- Decimal to Hexadecimal: Divide by 16 and retain the remainders.
- Hexadecimal to Decimal: Multiply each hex digit by 16 raised to its position from right (0 for rightmost) and sum the products.
Converting Fractions
- For fractional conversions, the standard method of using a base-10 representation must be translated for a different base, like base 2 or 8.
- Specific method depends if the number is before or after the decimal point.
Quantities and Counting
- Conversion tables for common decimal, binary, octal and hexadecimal values are presented in the slides.
Conversion Among Bases
- Illustrates possible conversions from decimal, binary, octal, to hexadecimal
Quick Example
- An example illustrating how these concepts are implemented in real use-cases is shown.
Decimal to Binary Conversion Technique
- Divide the decimal number by 2, and record the remainder.
- Repeat this process until the quotient becomes zero.
- Concatenate the remainders in reverse order to obtain the binary equivalent.
Example of Decimal to Binary Conversion
- An example of decimal to Binary conversion is displayed, showing the calculation steps and result.
Decimal to Fractional Binary Conversion Technique
- Multiply the fractional part of the decimal by 2.
- If the result is greater than or equal to 1, append a 1 and subtract 1 from the result.
- If the result is less than 1, append a 0 to the binary fractional part.
- Repeat until the result is exactly 0 or until you have reached a desired level of precision.
- Append the integer part to the binary fractional part, separated by a decimal point, to assemble the full binary result.
Binary Addition and Multiplication
- Binary addition is performed bit by bit and carries are propagated in the addition process
- Binary multiplication procedures for various values, similar to decimal arithmetic, but using 0s and 1s instead of base-10 digits.
- Charts that demonstrate two and n-bit value operations
Fractions (decimal and binary conversions)
- Decimal to decimal fraction examples.
- Binary to decimal fraction examples
Converting base 16 (Hexadecimal) to base 10 (Decimal)
- Multiply each hexadecimal digit by the appropriate power of 16 (starting from the rightmost digit).
Converting base 8 (Octal) to base 10 (Decimal)
- Multiply each octal digit by the appropriate power of 8 and sum the results.
Converting base 2 (Binary) to base 8 (Octal)
- Group the bits in sets of 3(From right to left). Add leading zeros if necessary.
- Convert each group of 3 binary digits into its respective octal equivalent.
Converting base 2 (Binary) to base 16 (Hexadecimal)
- Group the bits in sets of 4 (from right to left). Add leading zeros if necessary.
- Convert each group of 4 binary digits into its respective Hexadecimal equivalent.
Converting base 8 (Octal) to base 16 (Hexadecimal)
- Convert the octal number in the first step to binary.
- Then convert the binary number to hexadecimal.
Converting base 16 (Hexadecimal) to base 8 (Octal)
- Convert the hexadecimal number to binary.
- Then convert the binary number to octal.
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Description
Test your knowledge on different number systems including Decimal, Binary, Octal, and Hexadecimal. This quiz also covers the methods of converting between these bases. Challenge yourself to master the fundamental concepts of number representation and conversion techniques!
