Given a single-precision IEEE 754 representation of a floating point number as: 0x40700000, do the following: (a) Express the value of the S field in binary without spaces (count carefully). Do not abbreviate your answer. (b) Express the value of the E field in binary without spaces (count carefully). Do not abbreviate your answer. (c) Express the value of the F field in binary without spaces (count carefully). Do not abbreviate your answer.

Given a single-precision IEEE 754 representation of a floating point number as: 0x40700000, do the following: (a) Express the value of the S field in binary without spaces (count carefully). Do not abbreviate your answer. (b) Express the value of the E field in binary without spaces (count carefully). Do not abbreviate your answer. (c) Express the value of the F field in binary without spaces (count carefully). Do not abbreviate your answer.

EBK JAVA PROGRAMMING

9th Edition

ISBN:9781337671385

Author:FARRELL

Publisher:FARRELL

Chapter6: Looping

Section: Chapter Questions

Problem 8RQ

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Consider a new floating point representation, which we will call here the CMPT215Float16 representation. The CMPT215Float16 representation follows the IEEE 754 binary floating point standard, but with smaller-sized fields for the exponent and fraction. In particular, CMPT215Float16 numbers have a 1-bit sign field, followed by a 7-bit exponent field (in biased notation, with a bias of only 63 because of the smaller size of this field), followed by an 8-bit fraction field. Give, in decimal, the quantity represented by the following CMPT215Float16 floating point value: 0100001110100000.
You are asked to design a system of FP numbers representation (with your own design choices), labeled Custom_FP_48, for which we have 48 bits at our disposal in order to represent a number, in analogy with the IEEE 754 prototype. You are asked to provide: a) The types for evaluating this number b) The width of representation of these numbers (upper and lower) c) The maximum precision (i.e., the minimum difference between two successive numbers).
MCQS so now carefully read the question and give the most appropriate answer. a) If the following binary number were to be represented in the IEEE-754 single precision floating point format, then what would be the value of the exponent field in binary. 10111010.0101 b) If the following binary number were to be represented in the IEEE-754 single precision floating point format, then what would be the binary value stored in the sign bit. 10111010.0101 c) Convert the decimal number 1.1 into its equivalent binary representation. d) The maximum value in hexadecimal that can be stored in a single byte is e) If the following binary number were to be represented in the IEEE-754 single precision floating point format, then what would be the binary value that would be stored in the significand part. 10111010.0101 f) The sum of the following two octal values, 77 and 56 can be expressed in octal as:
If you have access to the natural log function ln(x), specify how you could use it to implement a log(b, x) function where b is the base of the log. What should the function do for negative b values? Assume an IEEE floating point implementation.
a. Explain the Criteria based on which Pseudorandom Numbers are differentiated from True Random Numbers. b. ,True Random Number Generator (TRNG) are often used in combination/support with Pseudorandom Number Generator (PRNG). Explain the purpose and the benefits of such arrangement.
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What is "Approximation Error" in floating-point representation? Why is it happening?
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2. Say you're working in a floating point system with base () of 2, precision (p) of 3 and allowable exponents (e) from -1 to 1, as we discussed in class. There are only 25 numbers you can represent in this system. What are they? Remember that every number in a floating point system can be represented as +...+ Where d, =1 and d;=the i digit out of p-1 digits that the computer uses to store the number.
a. Give an example of a value that can't be represented in 32-bit IEEE because it doesn't have a finite representation in binary. Explain (i.e. show that it doesn't have a finite representation). b. Give an example of a value that can't be represented in 32-bit IEEE because it's out of the range of values that can be represented in this format. Explain (i.e. show that this value is out of the range of expressible values of 32-bit IEEE 754).
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