How many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code?

Answers

Answer 1

Note that powers of 2 can be written in binary as

[tex]2^0=1_2[/tex]
[tex]2^1=10_2[/tex]
[tex]2^2=100_2[/tex]

and so on. Observe that [tex]n+1[/tex] digits are required to represent the [tex]n[/tex]-th power of 2 in binary.

Also observe that

[tex]\log_2(2^n)=n\log_22=n[/tex]

so we need only add 1 to the logarithm to find the number of binary digits needed to represent powers of 2. For any other number (non-power-of-2), we would need to round down the logarithm to the nearest integer, since for example,

[tex]2_{10}=10_2\iff\log_2(2^1)=\log_22=1[/tex]
[tex]3_{10}=11_2\iff\log_23=1+(\text{some number between 0 and 1})[/tex]
[tex]4_{10}=100_2\iff\log_24=2[/tex]

That is, both 2 and 3 require only two binary digits, so we don't care about the decimal part of [tex]\log_23[/tex]. We only need the integer part, [tex]\lfloor\log_23\rfloor[/tex], then we add 1.

Now, [tex]2^9=512<1024=2^{10}[/tex], and 999 falls between these consecutive powers of 2. That means

[tex]\log_2999=9+\text{(some number between 0 and 1})[/tex]

which means 999 requires [tex]\lfloor\log_2999\rfloor+1=9+1=10[/tex] binary digits.

Your question seems to ask how many binary digits in total you need to represent all of the numbers 0-999. That would depend on how you encode numbers that requires less than 10 digits, like 1. Do you simply write [tex]1_2[/tex]? Or do you pad this number with 0s to get 10 digits, i.e. [tex]0000000001_2[/tex]? In the latter case, the answer is obvious; [tex]1000\times10=10^4[/tex] total binary digits are needed.

In the latter case, there's a bit more work involved, but really it's just a matter of finding how many number lie between successive powers of 2. For instance, 0 and 1 both require one digit, 2 and 3 require two, while 4-7 require three, while 8-15 require four, and so on.

Answer 2

Final answer:

To represent the decimal numbers from 0 to 999 in binary code, we require 10 bits. This is determined by finding the binary equivalent of the largest number, 999, which necessitates at least 10 powers of 2 (from [tex]2^0 \ to \ 2^9[/tex]).

Explanation:

To determine how many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code, we need to find the binary equivalent of the largest number in that range, which is 999. In binary, this would require the highest power of 2 that is less than or equal to 999. The largest power of 2 less than 999 is 512 (29), and we continue to add powers of 2 to represent the number:

512 (29)
256 (28)
128 (27)
64 (26)
32 (25)
16 (24)
8 (23)
4 (22)
2 (21)
1 (20)

Adding these up, we see that we need at least 10 bits to represent the number 999 in binary, because adding powers of 2 from 20 to 29 will give us the required range. Therefore, we need 10 bits to represent any number from 0 to 999 in binary.

Related Questions

Write in expanded form. Use parentheses to indicate multiplication. (2r) 5

Answers

2 x 5 x r will give you this as well as 10r

If I assume correctly, the eqaution you ment to write is (2r)^5. If I am correct the answer your looking for is (2r)(2r)(2r)(2r)(2r) Hope this help ;-)

A tree 24 feet tall casts a shadow 12 feet long.Brad is 6 feet tall. How long is Brads shadow

Answers

Answer: 6

Step-by-step explanation:

thiss is for a challenge

In complete two or more sentences, determine the appropriate model for the given data and explain how you made your decision. (1,0), (2,1.5), (5,2.5), (8,3)

Answers

https://brainly.com/question/8848974
see if this helps

Answer:

The model for the given point is [tex]y=1.4004\ln (x) + 0.2158[/tex]

Step-by-step explanation:

Given : Data (1,0), (2,1.5), (5,2.5), (8,3).

To find : Determine the appropriate model for the given data?

Solution :

Data (1,0), (2,1.5), (5,2.5), (8,3).

We plot the data points on the graph and get the best fit line using trend line of the function.

Using regression calculator,

The function has a logarithmic behavior so the best line which represent the data is given by

[tex]y=1.4004\ln (x) + 0.2158[/tex]

and the value of R² i.e. correlation coefficient is given by

[tex]R^2=0.9691[/tex] which is approximately equal to 1 gives you the best fit line.

Therefore, The model for the given point is [tex]y=1.4004\ln (x) + 0.2158[/tex]

Refer the attached figure below.

Can someone solve this please?

Answers

2x = 8 - 5y
x = 8/2 - 5y/2
x = 4 - 2.5 y
or
x = 4 - 5/2 y

Determine the equation for the parabola graphed below.

Answers

The generic equation of a parabola is:
f (x) = ax ^ 2 + bx + c
To verify the equation of the parabola you need three points:
f (x) = ax ^ 2 + bx + c
We choose the points:
(x, y) = (- 1,7)
7 = a (-1) ^ 2 + b (-1) + c
7 = a - b + c
(x, y) = (0,5)
5 = a (0) ^ 2 + b (0) + c
5 = c
(x, y) = (- 2,5)
5 = a (-2) ^ 2 + b (-2) + c
5 = 4a - 2b + c
We solve:
c = 5
5 = 4a - 2b + 5
7 = a - b + 5
Rewriting
b = 2a
a-b = 2
Substituting:
a-2a = 2
a = -2
b = -4
The equation of the parabola is:
f (x) = - 2x ^ 2 -4x + 5

A gear rotates i degree each second. If it rotates for 2 minutes, how many degrees will it measure

Answers

There are 120 seconds in 2 minutes. The gear will turn 120°.

The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments with lengths in the ratio 1:2. the length of the altitude is 8. how long is the hypotenuse

Answers

1. By the Altitud Rule, you have:

Segment1/Altitud=Segment 2/Altitud

2. The ratio is 1:2, then:

Segment1=2x

Segment2=1x
Segment2=x

Altitud=8

3. When you apply the Altitud Rule, you obtain:

Segment1/Altitud=Segment 2/Altitud
2x/8=8/x

4. When you clear the "x", you have:

(2x)(x)=(8)(8)
2x²=64
x²=64/2
x²=32
x=√32
x=4√2

5. Then:

2x=2(4√2)=8√2

6. Therefore, the lenght of the hypotenuse is:

h=4√2+8√2
h=12√2
h=16.97

The hypotenuse is 17.1 inches long

Given that the scale ratio is 1 : 2.

This means that:

Segment 1 : Segment 2 = 1 : 2

This gives

Segment 1 : Segment 2 = x : 2x

By comparison,

Segment 1 = x

Segment = 2x

Using the Altitude rule, x is then calculated as:

[tex]\frac{Segment\ 2}{8} = \frac{8}{Segment\ 1}[/tex]

Substitute known values

[tex]\frac{2x}{8} = \frac{8}{x}[/tex]

Cross multiply

[tex]2x^2 = 64[/tex]

Divide through by 2

[tex]x^2 = 32[/tex]

Take the square root of both sides

[tex]x = 5.7[/tex]

The length of the hypotenuse (h) is then calculated as:

[tex]h =x + 2x[/tex]

[tex]h =3x[/tex]

[tex]h =3 * 5.7[/tex]

[tex]h =17.1[/tex]

Hence, the hypotenuse is 17.1 inches long

Answers

possible options are 1 7, 2 5, 3 4
it would be 3 and 4 since they are the only two in here that have the least common denominate of 12. 5 isn't divisible by 12, 7 isn't either, so that only leaves 3 and 4 and they worked since 3*4 does equal 12.

How many lines of a reflectional symmetry does a equilateral triangle have?

Answers

I believe the correct answer is 3.

Answer:

Equilateral triangle has 3 Reflection symmetry.

Step-by-step explanation:

Given : Equilateral triangle.

To find : How many lines of a reflectional symmetry does a equilateral triangle have.

Solution : We have given a equilateral triangle.

Equilateral triangle :triangle which has all three sides and angles are equal.

Reflection symmetry : If we reflect any shape of figure it gives same shape .

Therefore, Equilateral triangle has 3 Reflection symmetry.

50 students live in a dormitory. the parking lot has the capacity for 30 cars. if each student has a car with probability 12 (independently from other students), what is the probability that there won't be enough parking spaces for all the cars?

Answers

Final answer:

To find the probability that there won't be enough parking spaces for all the cars, we can use the binomial distribution formula and calculate the probability of having more than 30 cars in a sample of 50. The probability is approximately 0.9999999999.

Explanation:

To find the probability that there won't be enough parking spaces for all the cars, we need to find the probability that the number of cars exceeds the capacity of the parking lot. The number of cars follows a binomial distribution with a probability of success of p = 0.12 and a sample size of n = 50. We can use the binomial probability formula to calculate this probability:

P(X > 30) = 1 - P(X ≤ 30)

where P(X ≤ 30) is the probability that the number of cars is less than or equal to 30. We can use a binomial calculator or software to find this probability:

P(X > 30) ≈ 0.9999999999

Ms.michaels made an apple pie with a radius of 5in .she cut the pie into 6 equal slices. Fined the approximate area of each slice.

Answers

The answer is sim ple it is 0.83333333333 etc.

now, area of a circle is A = πr², where r = radius.

we know the radius is 5, thus the area of the whole circle is A = π5² or 25π.

then each slice is just one sixth of that, thus 25π/6 is the area of one slice.

misha has a board that is 17 1/2 inches long that he has to cut into 3 equal pieces how long should each piece be

Answers

Divide total length by 3.

=17 1/2 ÷ 3
convert to improper fraction
= 35/2 ÷ 3
multiply by reciprocal of 3
= 35/2 * 1/3
= 35/6
= 5 5/6

ANSWER:
Each piece should be 5 5/6 inches.

Hope this helps! :)

A drum of oil has a height of 4ft and a radius of 1.2ft The cost of oil $22 per cubic feet.What is the cost to fill the drum of oil

Answers

check the picture below.

The length of a rectangular prism is 4 feet, and the width is 3 feet. The volume of the prism is 9 cubic feet. In inches, what is the height of the prism?

Answers

The height of the prism would be 0.75

How was triangle A translated?

Answers

If we translate an object, we move it up or down or from side to side. But we do not change its shape, size or direction. Which of the following triangles (P, Q or R) is atranslation of triangle ABC? ... P is not a translation of triangle ABC because the object and its image are facing in opposite directions.

Rachel has 60 scones. She sells them to Robbie, Cameron, Louis, Tom and Charlie in that order. Each customer buys more scones than the last and the increase is the same number in each case. Robbie and Cameron’s combined total number of scones is three sevenths of the total of Louis, Tom and Charlie. How many scones does each boy buy?

Answers

Answer:

Robbie: 6
Cameron: 9
Louis: 12
Tom: 15
Charlie: 18

Explanation:

1) Assume that Rachel sold all the cones: 60

2) Call x the amount that Robbie bought and d the constant increase on the purchse.

3) That means that the number of cones bought by each one is:

Robbie:            x
Cameron:         x + d
Louis:               x + d + d = x + 2d
Tom:                 x + 2d + d = x + 3d
Charlie             x + 3d + d = x + 4d

The sum of that is: x + (x + d) + (x + 2d) + (x + 3d) + (x + 4d) = 5x + 10d = 60

5x + 10d = 60 may be simplified by dividing each side by 5 => x + 2d = 12.

Equation (1) x + 2d = 12

4) Robbie and Cameron’s combined total number of scones is three sevenths of the total of Louis, Tom and Charlie

=> x + (x + d) = [3/7] [ (x + 2d) + (x + 3d) + (x + 4d) ]

=> 2x + d = [3/7] (3x + 9d)

=> 7(2x + d) = 3 (3x + 9d)

=> 14x + 7d = 9x + 27d

=> 14x - 9x = 27d - 7d

=> 5x = 10d

=> x = 2d

Equation (2) x = 2d

5) Now you just have to solve this simple system of equations:

x + 2d = 12

x = 2d

Subitituing x for 2d in the first equation: x + x = 12 => 2x = 12 => x = 6

Now replace x = 6 in any of the two equations and you get the value of d.

For example, from x = 2d => d = x / 2 = 6 /2 = 3.

6) Finally, calcualte the number of cones of each:

                                                                           Result
Robbie:            x                                                6
Cameron:         x + d                                          6 + 3 = 9
Louis:               x + d + d = x + 2d                      9 + 3 = 12
Tom:                 x + 2d + d = x + 3d                   12 + 3 = 15
Charlie             x + 3d + d = x + 4d                    15 + 3 = 18
                                                                -----------------------------------------
Total                                                                   6 + 9 + 12 + 15 + 18 = 60

For each pair of numbers, tell: By what percent of the first number is the second number larger? By what percent of the second number is the first number smaller? 100 and 110

Answers

Final answer:

The second number, 110, is 10 percent larger than the first number, 100. Conversely, the first number, 100, is approximately 9.09 percent smaller than the second number, 110.

Explanation:

To find by what percent the second number is larger than the first, we calculate the difference between the two numbers and then divide by the first number, multiplying the result by 100. For the numbers 100 and 110:

Subtract the first number from the second: 110 - 100 = 10.

Divide the difference by the first number: 10 / 100 = 0.10.

Multiply by 100 to find the percentage: 0.10 * 100 = 10 percent.

Now, to find by what percent the first number is smaller than the second number:

Again, find the difference: 110 - 100 = 10.

But this time, divide by the second number: 10 / 110 = ~0.0909.

Multiply by 100 to find the percentage: ~0.0909 * 100 = approximately 9.09 percent.

Therefore, 110 is 10 percent larger than 100, while 100 is approximately 9.09 percent smaller than 110.

A section in a stained glass window is shaped like a trapezoid. The top base is 1 centimeter and the bottom base is 1.5 centimeters long. If the area of the section of glass is 5.5 square centimeters, how tall is the section?

Answers

4.4 square centimeters.

The partially complete anova table given here is for a two-factor factorial experiment source df ss ms factor a 3 2.25 0.75 factor b 1 0.95 interaction 3 0.30 error 16 2.40 0.15 total 6.50

Answers

Final answer:

The student's question involves understanding and completing a two-factor ANOVA table in statistics, which is used to determine if there are significant differences between group means.

Explanation:

The question involves an Analysis of Variance (ANOVA) table used in statistics to test if there are significant differences between the means of three or more independent groups. Given the degrees of freedom (df), sum of squares (SS), and mean squares (MS), one would typically calculate the F-statistic for each source of variance (Factor A, Factor B, and the interaction) by dividing the MS of that source by the error MS. If the calculated F-statistic is greater than the critical F-value from the F-distribution table, one can reject the null hypothesis that the group means are equal. ANOVA is used in various research fields where data needs to be compared across multiple groups or factors.

Wyatt is hiking a trail that is 11/12 mile long. After hiking 1/4 Mile he stops for water. How much farther must he hike to finish the trail?

Answers

d = 11/12 mile
stop = 1/4 mile
d_remaining = ?????
d_remaining =d - stop
d_remaining = 11/12 - 1/4
1/4 = 1*3 / 4*3 = 3/12 You are doing this so that 1/4 has the same denominator as 11/12
d_remaining = 11/12 - 3/12 = 8/12
Wyatt has 8/12 of a mile to go 8/12 = 2/3 of a mile to go
2/3 mile <<<<<==== Answer.

You could also do this as a decimal
11/12 = 11 divide by 12 = 0.91666666667
1/4 = 0.25
Remainder = 0.9166666667 - 0.25
Remainder = 0.6666666 which is 2/3
I have not been particularly careful about how many 6s you get. Just copy what your calculator says..

Final answer:

Wyatt has 2/3 mile left to hike to finish the 11/12 mile long trail after stopping for water having hiked 1/4 mile.

Explanation:

Wyatt is hiking a trail that is 11/12 mile long, and after hiking 1/4 mile, he stops for water. To calculate how much farther he must hike to finish the trail, we subtract the distance he has already hiked from the total length of the trail.

The calculation would be:

Total trail length - Distance already hiked = Distance remaining

(11/12) - (1/4) = (11/12) - (3/12) = (8/12) miles

After simplifying the fraction, we find that Wyatt has 2/3 mile left to hike to reach the end of the trail.

susan bought a 1 kilogram bag of grape. on the way home, she ate 125 grams of the grapes. how many grams of grapes does susan have left?

Answers

1 kilogram = 1000 grams

1000 - 125 = 875g

Susan has 875g of grapes left.

Susan has 875 grams of grape left

How to determine the amount left?

The given parameters are:

Amount bought = 1 kgAmount ate = 125 grams

The amount left is:

Amount left = 1 kg - 125 grams

Express kg as grams

Amount left = 1000 grams - 125 grams

Evaluate the difference

Amount left = 875 grams

Hence, Susan has 875 grams of grape left

Answers

In general 2^n is the number of pieces of information n bits can store.

(a) Antonio can use the formula 2^n-1 to indicate the maximum size of numbers an n-bit word can store.
(b) for a 16-bit system, the maximum number of keys Millie can collect is 2^(16)-1 = 65536-1=65535
(c) For a 14 byte program, there are 14*8=112 bits.

Final answer:

Antonio can use the formula 2ⁿ - 1 to calculate the number of golden keys Millie can collect in a 16-bit system, resulting in 65,535 keys. For the spreadsheet program taking up 14 TB of memory, this translates to 112 × 10¹² bits, illustrating the vastness of binary encoding in computing.

Explanation:

Understanding Antonio's Formulas and Calculations

In the realm of computer programming and data representation, understanding how information is encrypted and the number of combinations possible for bits is crucial. Here, we'll explore Antonio's approach to calculating the number of golden keys in a video game and translating memory size from terabytes to bits.

a. Formula Creation for Golden Keys

Antonio is developing a video game where the main character collects golden keys. The number of possible arrangements of bits in the system is represented by 2n, where n represents the number of bits. Therefore, to find the maximum number of keys Millie can collect, which is one less than the total number of bit arrangements, Antonio can use the formula 2ⁿ - 1.

b. Calculating Golden Keys in a 16-bit System

At a 16-bit system, the number of possible arrangements is 216 = 65,536. Following Antonio’s formula, Millie can collect 65,536 - 1 = 65,535 golden keys.

c. Bits in Antonio's Spreadsheet Program

For a program taking up 14 terabytes (TB) of memory, with each byte equating to 8 bits, we need to first convert terabytes to bytes then to bits:

One TB equals 1012 bytes.

Therefore, 14 TB equals 14 × 10¹² = 14 × (1012 bytes).

Converting to bits (by multiplying by 8): 14 × 10¹² × 8 = 112 × 10¹² bits.

This calculation illustrates how memory size translates into a vast number of bits, reflecting the exponential nature of binary encoding used in computing and data storage.

19.21 is 113% of what number

Answers

113% as in decimal form is 1.13, 19.21 divided by 1.13 is 17.

19.21 is 113% of 17

113% of x = 19.21

(113/100)x = 19.21

(1 13/100)x = 19.21

19.21 divides by 1 is the same value l

13/100 x = 19.21

Divide both sides by 13/100 or 0.13 to find the answer.

Give me an expression that is equal to 4(6j + 5 + 2j). I already got 4(8j + 5), can you get me another expression using the distributive property? Once you got the answer give me the answer you got and translate it into a verbal expression

Answers

24j + 20 + 8j
twenty-four j plus twenty plus eight j

OR

32j + 20
Work: 24j + 8j = 32

thirty-two j plus twenty

Hope this helps!

Yoko is buying a car from a local car dealership. She wants to get the lowest interest rate possible. Which will most likely help her get the lowest interest rate? asking nicely making sure she has a positive credit history explaining that she has many outstanding loans showing her driver’s license

Answers

Answer: The answer is (b) making sure she has a positive credit history.

Step-by-step explanation: Given that Yolo is buying a car from a local car dealership and wants to get the lowest interest rate possible. We are to select the correct option which will most likely help her.

From the given options, we can see that she will get the lowest interest rate possible if she has a positive credit score.

Thus, (b) is the correct option.

She should [tex]\boxed{{\text{make sure that she has a positive credit history}}}[/tex] to get the lowest interest rate possible. Option (b) is correct.

Further Explanation:

Given:

The options are as follows,

(a). Asking nicely

(b). Making sure she has a positive credit history

(c). Explaining that she has many outstanding loans

(d). Showing her driver’s license

Explanation:

Yoko is buying a car from a local car dealership. She wants to get the lowest interest rate possible.

To obtain the lowest interest rate she should ask the dealer for lowest interest rate and make sure that she has a positive credit history.

She should [tex]\boxed{{\text{make sure that she has a positive credit history}}}[/tex] to get the lowest interest rate possible. Option (b) is correct.

Option (A) is not correct.

Option (B) is correct.

Option (C) is not correct.

Option (D) is not correct.

Learn more:

Learn more about inverse of the function https://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Credit Risk

Keywords: Yoko, buying, car, local car, dealership, lowest interest rate, possible, asking nicely, credit history, positive credit history, loan, license, outstanding.

why aren't voluntary response samples usually representative of the population

Answers

voluntary responses simply means, someone approaches you and say "hey, let me give you my take on this or that topic", and they "volunteer" their response to you.

now, the people that will approach you, are just the people that will approach you, it could be all from one specific group, say all women, or mostly women, or mostly doctors, or mostly certain group, and therefore, they'll be giving their take on the topic, but for all we know they're just 15% of the whole population, it just so happen that they approach you.

and if they're 15% of the population, then their opinion matters only at the 15% consideration for the topic.

Answer: it would be (the people who volunteer usually have a motive to do so and will be the ones represented

Step-by-step explanation:

your welcome

Hello i need help on this one and giving away points+ brainiest on the legit answer thanks!

Answers

After you multiply by 16'6", you find the answer is
.. L = 2 × 2'6" = 5'

The number that goes in the box is 5.

_____
16'6" is exactly twice as long as 8'3". You don't even have to convert to inches or decimal feet to see that.

I thin the answer is 5 thank you

The purchase price of an IPad is 650. What is the total price oif the sales tax rate is 8%

Answers

650 x 1.08 = 702

total price = $702

Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn, and rode 3 miles to the local swimming pool. If he had ridden directly to the pool, how much distance would he have saved? Round the answer to the nearest tenth of a mile.
Pick one;
1.2 miles
1.8 miles
2.5 miles
4.2 miles
(Ps: I can't copy the picture but its a right triangle.)

Answers

For this case we can model the problem as a rectangle triangle.
We know:
Length of the sides of the triangle
We want to know:
Length of the hypotenuse
Using the Pythagorean theorem we have:
[tex]d = \sqrt{3^2 + 3^2} [/tex]
Rewriting the expression we have:
[tex]d = \sqrt{2(3^2)} [/tex]
[tex]d = 3\sqrt{2} [/tex]
[tex]d = 4.2 miles [/tex]
Then, the distance that he would have saved if he travels directly is:
[tex]3 + 3 - 4.2 = 1.8 miles [/tex]
Answer:
he would have saved:
1.8 miles

Answer:

1.8 miles

Step-by-step explanation:

A cylinder shaped water tank has a diameter of 8 m and a height of 20 m. What volume of water does the tank contain when it is 60% full? Use 3.14 to approximate pi. Enter your answer as a decimal to the hundredths place in the box.
____ m³

Answers

the volume of a cylinder is the area of the base times the height
area of the base: 3.14*4² (diameter is 8, so radius is 4)
height: 20
3.14*4²*20=1004.8
60% of 1004.8=602.88

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