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: cannot emit light and has speed limitations

Explanation:

Silicon is usually used in computer chips and solar cells but Gallium arsenide is regarded as a better alternative even though it's costly than silicon.

Gallium arsenide has technical advantages over silicon as its electrons

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Answer:

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Explanation:

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O The attachment will always appear in the body of the message.
O The paperclip icon indicates an attached file.
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Answers

Answer:

This program is as follows

total = 0; count = 0

testscore = int(input("Score: "))

while testscore != 999:

   if testscore < 0 or testscore > 100:

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   else:

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       count+=1

   testscore= int(input("Score: "))

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Explanation:

This initializes total and count to 0

total = 0; count = 0

This gets input for score

testscore = int(input("Score: "))

The following iteration stop when 999 is entered

while testscore != 999:

This prints out of range for scores outside 0 - 100

   if testscore < 0 or testscore > 100:

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Otherwise

   else:

The total score is calculated

       total+=testscore

The number of score is calculated

       count+=1

Get another input

   testscore = int(input("Score: "))

The number of score is printed

print(count,"scores entered")

The average of score is printed

print("Arithmetic Average:",total/count)

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Answers

Answer:

"Virtual reality" is the appropriate answer.

Explanation:

The utilization of technological advances gives the impression of a 3D interactive environment wherein the things that have such a perception of space embodiment or involvement, are considered as Virtual reality.

Virtual reality implementations often include:

Entertainment,Medical and Educational activities.

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Explanation:

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Explanation:

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Answers

Answer:

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Explanation:

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for i = 1 to 7

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[Convert to degree Fahrenheit]

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Answers

Resposta:

44,76 Kwh

Explicació:

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Per tant, 30 cavalls es convertiran en:

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Temps = 2 hores

La quantitat d'energia consumida s'obté mitjançant la relació:

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Answers

Answer: B. system accounts, contingent IDs

Explanation:

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Answers

Answer:

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Answers

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Explanation:

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Answer:

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Answer:

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Edit : nvm i got what you were saying ...

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Answer:

true

Explanation:

because Internet

because Internet

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Answers

Answer:

Option D

Explanation:

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Answers

Answer:

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Explanation:

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Answers

Answer:

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Explanation:

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Answers

Answer:

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Explanation:

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Answers

[tex]{\blue{OII}}[/tex]

[tex]{\green{TUDO}}[/tex] [tex]{\red{BEM ?}}[/tex]

The activities that the computer scientist develops Data structuring, development and design. CG. Numerical analysis and development of algorithms. Database management. CG.

[tex]{\red{TCHAU }}[/tex]

❤❤

With ok g hey Ed F egg to TK up TK A

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Answers

Answer:

end user

Explanation:

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Answers

Answer:

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Answers

Answer:

SRC: it specifies the URL of the image

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Answers

Answer:

The base case

Explanation:

Required

The part that determines the termination of a recursion

This part of a recursion is referred to as the base case.

Take for instance, the following:

factorial(int n) {

   if (n < = 1) {         return 1; }

   else {             return n*factorial(n-1);    }  }

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Answers

Answer: round-trip time

message byte size.

Explanation:

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Answers

Answer:

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Answers

Answer:

El signo =.

Explanation:

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Además, dentro de sus celdas existe la posibilidad de realizar fórmulas, que emulan las fórmulas matemáticas y realizan cálculos específicos entre distintas celdas.

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