What is the bit pattern (raw binary) of the single precision representation of the decimal number 0.125 following IEEE 754 standard

Answers

Answer 1

Answer:

The three elements that make up the number's 32 bit single precision IEEE 754 binary floating point representation:

Sign (1 bit) = 0 (a positive number)

Exponent (8 bits) = 0111 1100

Mantissa (23 bits) = 000 0000 0000 0000 0000 0000

Explanation:

1. First, convert to the binary (base 2) the integer part: 0.

Divide the number repeatedly by 2.

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.

division = quotient + remainder;

0 ÷ 2 = 0 + 0;

2. Construct the base 2 representation of the integer part of the number.

Take all the remainders starting from the bottom of the list constructed above.

0(10) = 0(2)

3. Convert to the binary (base 2) the fractional part: 0.125.

Multiply it repeatedly by 2.

Keep track of each integer part of the results.

Stop when we get a fractional part that is equal to zero.

#) multiplying = integer + fractional part;

1) 0.125 × 2 = 0 + 0.25;

2) 0.25 × 2 = 0 + 0.5;

3) 0.5 × 2 = 1 + 0;

4. Construct the base 2 representation of the fractional part of the number.

Take all the integer parts of the multiplying operations, starting from the top of the constructed list above:

0.125(10) =

0.001(2)

5. Positive number before normalization:

0.125(10) =

0.001(2)

6. Normalize the binary representation of the number.

Shift the decimal mark 3 positions to the right so that only one non zero digit remains to the left of it:

0.125(10) =

0.001(2) =

0.001(2) × 20 =

1(2) × 2-3

7. Up to this moment, there are the following elements that would feed into the 32 bit single precision IEEE 754 binary floating point representation:

Sign: 0 (a positive number)

Exponent (unadjusted): -3

Mantissa (not normalized):  1

8. Adjust the exponent.

Use the 8 bit excess/bias notation:

Exponent (adjusted) =

Exponent (unadjusted) + 2(8-1) - 1 =

-3 + 2(8-1) - 1 =

(-3 + 127)(10) =

124(10)

9. Convert the adjusted exponent from the decimal (base 10) to 8 bit binary.

Use the same technique of repeatedly dividing by 2:

division = quotient + remainder;

124 ÷ 2 = 62 + 0;

62 ÷ 2 = 31 + 0;

31 ÷ 2 = 15 + 1;

15 ÷ 2 = 7 + 1;

7 ÷ 2 = 3 + 1;

3 ÷ 2 = 1 + 1;

1 ÷ 2 = 0 + 1;

10. Construct the base 2 representation of the adjusted exponent.

Take all the remainders starting from the bottom of the list constructed above:

Exponent (adjusted) =

124(10) =

0111 1100(2)

11. Normalize the mantissa.

a) Remove the leading (the leftmost) bit, since it's allways 1, and the decimal point, if the case.

b) Adjust its length to 23 bits, by adding the necessary number of zeros to the right.

Mantissa (normalized) =

1 000 0000 0000 0000 0000 0000 =

000 0000 0000 0000 0000 0000

12. The three elements that make up the number's 32 bit single precision IEEE 754 binary floating point representation:

Sign (1 bit) = 0 (a positive number)

Exponent (8 bits) = 0111 1100

Mantissa (23 bits) = 000 0000 0000 0000 0000 0000


Related Questions

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Answer:

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Explanation:

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Answer:

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>>>

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Explanation:

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Answer:

a) phone

b)

c) cascading style

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Answer:

USB

Explanation:

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[tex]\huge\mathcal{\fcolorbox{aqua}{azure}{\red{✿ʏᴏᴜʀ- ᴀɴsᴡᴇʀ ♡❖}}}[/tex]

A Medication Administration Record (MAR, or eMAR for electronic versions), commonly referred to as a drug chart, is the report that serves as a legal record of the drugs administered to a patient at a facility by a health care professional. The MAR is a part of a patient's permanent record on their medical chart

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[tex]\boxed{\pmb{\green{\sf{MAR}}}}[/tex]

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You make a purchase at a local hardware store, but what you've bought is too big to take home in your car. For a small fee, you arrange to have the hardware store deliver your purchase for you. You pay for your purchase, plus the sales taxes, plus the fee. The taxes are 7.5% and the fee is $20. (i) Write a function t(x) for the total, after taxes, on the purchase amount x. Write another function f(x) for the total, including the delivery fee, on the purchase amount x. (ii) Calculate and interpret (f o t)(x) and (t o f )(x). Which results in a lower cost to you

Answers

Answer:

[tex]f(x) = 1.075x[/tex]

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Explanation:

Given

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[tex]Fee = \$20[/tex] -- delivery

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This is calculated as:

[tex]f(x) = Tax *(1 + x)[/tex]

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[tex]f(x) = x * (1 + 7.5\%)[/tex]

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[tex]f(x) = x * 1.075[/tex]

[tex]f(x) = 1.075x[/tex]

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[tex]t(x) = x + 20[/tex]

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[tex](f\ o\ t)(x) = f(t(x))[/tex]

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[tex]f(x) = 1.075x[/tex]

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[tex]f(t(x)) = 1.075t(x)[/tex]

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[tex]f(t(x)) = 1.075*(x + 20)[/tex]

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[tex]f(t(x)) = 1.075x + 21.5[/tex]

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We have:

[tex]t(x) = x + 20[/tex]

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[tex]t(f(x)) = f(x) + 20[/tex]

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[tex]t(f(x)) = 1.075x + 20[/tex]

We have:

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[tex](t\ o\ f)(x) = 1.075x + 20[/tex] --- This represents the function to pay tax on the item only

The x coefficients in both equations are equal.

So, we compare the constants

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Answers

Answer:

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Explanation:

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Answer:

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Explanation:

edge 2021

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Answer and Explanation:

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has replaced the need for landline telephones in many instance​

Answers

Explanation:

million landlines. During this same time the number of mobile phone lines that have been subscribed to has ...

Characteristics

write a program to check whether the number is odd or even using 'if' statement in python

Answers

Answer:

Python Program to Check if a Number is Odd or Even :

num = int(input("Enter a number: "))

if (num % 2) == 0:

print("{0} is Even number". format(num))

else:

print("{0} is Odd number". format(num))

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Answers

The utility that could be stored for the files is disk defragmenter.

The following information related to the disk defragmenter is:

In the case when the program saved the file on the disk so here the file should be put onto the empty space. It considered all the parts & pieces on each and every file and the same should be stored in one place.Also, the programs should be kept in one place, and the space that is not used should be on the hard disk.

Therefore we can conclude that The utility that could be stored for the files is disk defragmenter.

Learn more about the disk here: brainly.com/question/12656426

Type the correct answer in each box. Spell all words correctly.

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Answer:

1. Tablet

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Explanation:

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Answer:

ok let me try

It stands for

Hypertext Markup Language

Image result for html stands for

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Answers

Explanation:

Using Ohm's Law and a bit of substitution, we can solve for current.

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Answers

Answer:

Serial SCSI

Explanation:

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Answers

Answer:

Key escrow.

Explanation:

Cyber security can be defined as preventive practice of protecting computers, software programs, electronic devices, networks, servers and data from potential theft, attack, damage, or unauthorized access by using a body of technology, frameworks, processes and network engineers.

In Cyber security, encryption is a form of cryptography and typically involves the process of converting or encoding informations in plaintext into a code, known as a ciphertext.

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Answers

Answer:

SQL injection

Explanation:

SQL (Structured Query Language) Injection, are vulnerabilities associated security of SQL web interface through which an attacker can intrude into the backend of a database by modifying the queries a web program sends to the database to which it is connected

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Answers

In C++, 'Try block' comprises of a group of statements in which there is a probability of an exception to take place.

C). The statements that would be left in the try block in case a particular statement leads to an exception 'can't be executed.'

In case an exception takes place, the left statements in the try block fail to function. This is the primary reason for which a catch block immediately succeeds a try block in order to deal with the exception and help close that code to allow the statements to work. Thus, option C is the correct answer.

Learn more about 'Try block' here:

brainly.com/question/14186450

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Answers

Answer:

The most probable negative impact that IoT devices can have on users is the increase vulnerability of information technology cybersecurity, being that access can be gained into the system through another device connected to an IoT device from which it is theoretically possible to launch malicious computer codes, using both old and present day hacking technologies, due to the different securities, categories and systems of devices connected to the IoT

Explanation:

The negative impacts of Internet of Things IoT devices on users are

1) Loss of privacy 2) Network complexity increase 3) Increase in the dependence on technology 4) Increased unemployment, 5) Lack of compatibility between devices

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