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9(What is the binary representation of 0.1 − x?
I am reading the book CS:APP3 and in the chapter about floating point numbers there is a task about the number 0.1 in binary form. I figured out how to represent it in binary form. The number is represented with 23 bits after the decimal point. Then the questions are asked.
1. What is the binary representation of 0.1 - x?
2. What is the approximate decimal value of 0.1 - x?
x = 0.00011001100110011001100 binary)
The solution says that 0.1 - x has a binary representation: 0.000000000000000000000001100[1100]...
Why did the 23 bits after the decimal point become zero?
For the second question it says that the difference is 2^-20 x 1/10, i.e. .54 x 10^-8
—————————————————
Help me understand this situation. Why is 0.1 - x represented this way? How is it calculated correctly?
And how is the second question properly calculated?
I can't figure it out on my own.
#technology
source
I am reading the book CS:APP3 and in the chapter about floating point numbers there is a task about the number 0.1 in binary form. I figured out how to represent it in binary form. The number is represented with 23 bits after the decimal point. Then the questions are asked.
1. What is the binary representation of 0.1 - x?
2. What is the approximate decimal value of 0.1 - x?
x = 0.00011001100110011001100 binary)
The solution says that 0.1 - x has a binary representation: 0.000000000000000000000001100[1100]...
Why did the 23 bits after the decimal point become zero?
For the second question it says that the difference is 2^-20 x 1/10, i.e. .54 x 10^-8
—————————————————
Help me understand this situation. Why is 0.1 - x represented this way? How is it calculated correctly?
And how is the second question properly calculated?
I can't figure it out on my own.
#technology
source
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