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What is the binary equivalent of the decimal number 11111?
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Binary equivalent of 11111 does not make sense as 11111 is already in binary.
Explain the difference between decimal and binary number systems.
The decimal number system uses base 10 and includes digits 0-9. The binary number system uses base 2 and includes digits 0 and 1. Each digit in binary represents a power of 2, whereas in decimal they represent powers of 10.
What is the binary representation of the decimal number 19?
10011
What caution should be taken when comparing two floating point numbers directly (x == y)?
Direct comparison of floating point numbers should be avoided due to potential tiny differences caused by precision limits. Instead, a tolerance method (e.g., `abs(x - y) < epsilon`) should be used.
How do you handle negative decimal numbers when converting to binary?
Flag the number as negative, convert the absolute value to binary, and then represent the binary result with a negative sign or using two's complement for signed binary representation.
Why might floating point numbers not have exact representations in binary?
Floating point numbers may not have exact binary representations due to the finite number of bits available for their storage, leading to rounding errors and approximations.
How are decimal numbers expressed in computing? Provide an example.
Decimal numbers are expressed as a sum of powers of 10. Example: 302 = 3 * 10^2 + 0 * 10^1 + 2 * 10^0
What does 31 look like in binary?
31 in decimal is represented as 11111 in binary.
What is the binary representation of the decimal fraction 0.375?
0.011
Provide the steps to convert a decimal integer to binary.
1. Take the remainder when dividing the number by 2 (least significant bit). 2. Divide the number by 2 using integer division. 3. Repeat the process until the number is reduced to zero.
Describe the significance of the IEEE 754 standard for floating point arithmetic.
IEEE 754 standardizes the representation and behavior of floating point numbers, providing a consistent way to perform arithmetic computations across different computing systems, ensuring interoperability and reducing errors.
Why does Python round floating point numbers for display purposes?
Python rounds floating point numbers for display purposes to avoid showing long, imprecise representations and to provide results that are expected by users.
Explain the importance of tolerance method in floating point number comparison.
Tolerating method is important because floating point numbers may not have exact representations in binary, leading to potential inaccuracies. Using a tolerance method like `abs(x - y) < epsilon` helps in making precise computations.
What is a floating point number?
A floating point number is a number that has a decimal point and can represent fractions. In computing, it is used to represent real numbers with varying degrees of precision.
Describe the process to convert a decimal fraction to binary using the example of 0.375.
1. Multiply the fraction by a power of 2 to get a whole number (0.375 * 2^3 = 3). 2. Convert the resulting integer to binary (3 = 11). 3. Divide the binary integer by the same power of 2 (which is equivalent to shifting right by 3 places), resulting in 0.011.
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