All Questions
Tagged with floating-point number-systems
17
questions
0
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1
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53
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storing decimal number into computer with finite mantissa
I am learning about numerical methods and the following link caught my attention:
https://www.iro.umontreal.ca/~mignotte/IFT2425/Disasters.html
So from what I understand 0.1 is not exactly ...
- 109
0
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0
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257
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How to Add the IEEE 754 single-precision floating-point numbers from hexadecimal?
Question:
Add the following IEEE 754 single-precision floating-point numbers.
(a) C0123456 + 81C564B7
(c) 5EF10324 + 5E039020
I know I first need to convert to binary, then add and later change into ...
1
vote
1
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336
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In a floating-point system, is the unit roundoff $\epsilon_{mach}$ necessarily a machine number?
I have to answer the following questions:
(a)In a floating-point system, is the unit roundoff $\epsilon_{mach}$ necessarily a machine number? (Explain your answer or give a counterexample).
(b) Is ...
- 754
-2
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1
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96
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A question from floating point number representation.
The numbers in a floating-point system are defined by a base B, a mantissa length t, and an
exponent range [L, U]. A nonzero floating-point number x has the form
x = +/-(o.b1b2.....bt)B^e ---1
then ...
- 97
0
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1
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1k
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Hypothetical Computer Marc-32
I'm studying numerical analysis and i am stuck with one of my exercises. In the book "Numerical Analysis: Mathematics of scientific Computing" they introduce a hypothetical computer called MARC-32. In ...
1
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1
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3k
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Calculate the largest possible floating-point value: formula?
If I have a 32-bit representation of a floating-point where 1 bit is the sign, 8 bits are the exponent, and 23 bits make up the mantissa. The exponent notation is Excess-127.
...
1
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2
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3k
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Binary floating-point representation of 0.1
If $b=10$ and $p=3$, then 0.1 is represented as $1.00 × 1/10$. If $b=2$ and $p=24$, then 0.1 cannot be represented exactly, but is approximately
$$1.10011001100110011001101 × 1/2^4$$
Why do we ...
- 155
1
vote
1
answer
413
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What does leading $0s$ in a number in scientific notation mean?
Source: Computer Organization and Design: The Hardware/software Interface, David A. Patterson,John L. Hennessy
It doesn't seem as the author is using leading $0$ like leading $1$ in a matrix.
What ...
- 1,530
4
votes
2
answers
756
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How to understand or derive the formula "Mantissa bits${}/\log_2 10 ={}$ Decimal digits of precision"?
I asked a question a couple days ago about floating point precision on stackoverflow called, "Is floating point precision mutable or invariant?" and I received the following response.
The formula ...
- 161
0
votes
1
answer
475
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How can I add the following 32-bit IEEE floating-point numbers?
How can I add the following two 32-bit IEEE floating-point numbers in binary?
FEDCBA98(base 16) + 89ABCDEF(base 16)
= a 33-bit binary number.
How can this be possible?
- 91
0
votes
1
answer
87
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How would you convert the following 32-bit IEEE floating-point to decimal form?
I have got -1.101 1100 1011 1010 1001 1000 * 2^(9)
How can I convert this to decimal form?
- 91
1
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0
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1k
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smallest poisitive integer does not belong in floating point system F
A floating-point number system F is a subset of real numbers whose elements have the form:
$x=\pm(m/\beta^t)\beta^e$
base (beta), precision (t), and exponent range (emin and emax). The mantissa m ...
- 1,919
0
votes
1
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1k
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Converting double precision IEEE 754 hex to base 10 with repeating decimals
The number is 0x4001 8CCC CCCC CCCC.
So far I have the stored exponent as 1000000000 which equals ...
- 145
2
votes
1
answer
530
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Given the normalised floating point number system, calculate smallest possible value of y - x
First I present the problem and then my workings and thoughts:
Given the normalized floating point number system
$(\beta, t, L, U) = (10, 7, -6, 4)$ where $\beta$ is the base and $t$ is the ...
- 125
2
votes
1
answer
334
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Prove that in any base the number of digits composing the repetitive mantissa of the reciprocal of a prime $p$ never exceeds $p-1$.
I was trying to find bases where the reciprocals of primes have a short repetitive mantissa. Here is what I found:
The bases are on the left. The primes are at the top. The numbers represent the ...
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