SAT College

B(n)=2^n A binary code word of length n is a string of 0's and 1's with n digits. For example, 1001 is a binary code word of length 4. The number of binary code words, B(n), of length n, is shown above. If the length is increased from n to n+1, how many more binary code words will there be? The answer is 2^n, but I don't get how they got that answer. I would think 2^n+1 minus 2^n would be 2. Please help me! Thank you! ​

Answers

Answer 1

Answer:

The additional words is [tex]2^n[/tex]

Explanation:

Given

[tex]B(n) = 2^n[/tex]

Required

Determine the additional words; i.e. [tex]B(n + 1) - B(n)[/tex]

From the given parameters, we have that;

B is a function of n

Such that;

[tex]B(n) = 2^n[/tex]

To calculate [tex]B(n+1)[/tex], we simply substitute n + 1 for n

[tex]B(n) = 2^n[/tex]

[tex]B(n + 1) = 2^{n + 1}[/tex]

Applying laws of indices

[tex]B(n + 1) = 2^{n} * 2^1[/tex]

[tex]B(n + 1) = 2^{n} * 2[/tex]

[tex]B(n + 1) = 2(2^{n})[/tex]

Calculating Additional Binary Code;

[tex]B(n + 1) - B(n)[/tex]

Substitute values for B(n + 1) and B(n)

[tex]B(n + 1) - B(n) = 2(2^n) - 2^n[/tex]

Express [tex]2^n[/tex] as [tex]2^ n * 1[/tex]

[tex]B(n + 1) - B(n) = 2(2^n) - 2^n * 1[/tex]

Express 1 as [tex]2^0[/tex]

[tex]B(n + 1) - B(n) = 2(2^n) - 2^n * 2^0[/tex]

Factorize

[tex]B(n + 1) - B(n) = 2^n(2 - 2^0)[/tex]

[tex]B(n + 1) - B(n) = 2^n(2 - 1)[/tex]

[tex]B(n + 1) - B(n) = 2^n(1)[/tex]

[tex]B(n + 1) - B(n) = 2^n[/tex]

Hence, the additional words is [tex]2^n[/tex]

Related Questions

Lisa’s doctor tells her that she needs to eat more foods that contain calcium to maintain her bone health. What could happen if Lisa doesn’t follow her doctor’s orders

Answers

Answer:

b

Explanation:

yea

The official record of a high school student’s performance is called:

Answers

Answer:

A High School Transcript

Other Questions
help plz I think the first one is correct but I'm not sure ChemistryWhat is a chemical reaction Wingate Company, a wholesale distributor of electronic equipment, has been experiencing losses for some time, as shown by its most recent monthly contribution format income statement: Sales $ 1,546,000 Variable expenses 573,480 Contribution margin 972,520 Fixed expenses 1,070,000 Net operating income (loss) $ (97,480) In an effort to resolve the problem, the company would like to prepare an income statement segmented by division. Accordingly, the Accounting Department has developed the following information: Division East Central West Sales $ 416,000 $ 630,000 $ 500,000 Variable expenses as a percentage of sales 48 % 26 % 42 % Traceable fixed expenses $ 282,000 $ 324,000 $ 206,000 Required: 1. Prepare a contribution format income statement segmented by divisions. 2-a. The Marketing Department has proposed increasing the West Division's monthly advertising by $28,000 based on the belief that it would increase that division's sales by 13%. Assuming these estimates are accurate, how much would the company's net operating income increase (decrease) if the proposal is implemented? 2-b. Would you recommend the increased advertising? The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of 0.4. See the figure below. Suppose that the height of the candle after 11 hours is 16.6 centimeters. What was the height of the candle after 6 hours? "If a beam of monochromatic light is passed though a slit of width 15 m and the second order dark fringe of the diffraction pattern is at an angle of 5.2o from the central axis, what is the wavelength of the light?" If Ac={vt2/r) and vt=2 and r=2 find Aca. 4b. 2C. 1D. 8 Which device does Baldwin use when he says,"This fight begins, however, in the heart"?similefigurative languageANSWER: Figurative Language Indica si lo que dice el texto es cierto o falso.El objetivo de Cristbal Coln al salir del Puerto de Palos es llegar a la Repblica Dominicana. What is the value of a company's current assets if the company has \$5500$5500dollar sign, 5500 in inventory, \$1500$1500dollar sign, 1500 in prepaid expenses, \$8000$8000dollar sign, 8000 in current liabilities and a quick ratio of 0.70.70, point, 7 Read the following short passage and determine if it contains a fragmentBingham believed that these ruins were the Inca empire's last capital. Known as the lost city of the Incas."O A. No, this passage does not contain any fragments.O B. Yes, the fragment is "Bingham believed that these ruins were the Incaempire's last capital."OC. Yes, the fragment is Known as the lost city of the Incas.*** Nathan, a tutor, buys 5 calculators for $7.50 each at a store, planning to provide one to each of his clients. However, the next day, he discovers that the same calculators has gone on sale for $5.00 and also discovers that he will only have three tutoring clients instead of five. He returns the five calculators and purchases three calculators at the new sale price. He uses the following expression to determine the amount he should receive back from the store. (5 x $7.50) - (3 x $5.00) Which of the following expressions could Nathan have used. 5 ($7.50 - $5.00). $7.50 - $5.00. (5 x $7.50) - $5.00. (5 x $7.50) - $5.00. 3 ($7.50 - $5.00) +2 x $7.50 distinguish between Urban and rural poverty Why does a dog circle its bed before lying down? The "family resources" element of Family stress theory suggests that family-based resources such as cohesion, adaptability, and problem-solving may be important factors in whether families survive or deteriorate when stressors are introduced. Group of answer choices A movie theater is having a special. If a group of four pays $7.25 each for tickets, each person can get popcorn and a drink for $5.75. Use the expression 4(5.75 + 7.25) to find the total cost for 4 friends. Select the function completion that satisfies this docstring description: def convert_to_string(nums): """ (list of number) -> NoneType Replace each item in nums with its string equivalent. >>> nums 7. Diminishing returns to an input set in: A) when all inputs are fixed. B) when some inputs are fixed and some are variable. C) when all inputs are variable. D) only in the long run. What launched the era of modern science in the 17th century? A divorced woman with 2 young children has a small trust fund that gives her $2,500 a year in income. She collects another $2,500 per year in alimony payments. The woman wishes to make a contribution to an Individual Retirement Account this year. Which statement is TRUE If f(x)=ax^2+bx+c and f(0)=-4 and f(1)=-2 and f(2)=6, what is the value of A and B and C?