Binary numbers need more places for counting because: A. 0's and 1's can be added in front of them B. 0's and 1's have to be properly placed C. They are always big numbers D. Binary base is small E. None of the above
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- Sevens rule, zeros drooldef seven_zero(n):Seven is considered a lucky number in Western cultures, whereas zero is what nobody wants to be. We now bring these two opposites briefly together with positive integers that consist of some solid sequence of sevens, followed by some (possibly empty) solid sequence of zeros. Examples of such integers are 7, 77777, 7700000, 77777700, or 700000000000000. A surprising theorem proves that for any positive integer n, there exist infinitely many integers of such seven-zero form that are divisible by n. This function should return the smallest such seven-zero integer. This exercise is about efficiently generating all numbers of the constrained form of sevens and zeros in strictly ascending order to guarantee finding the smallest working such number. This logic might be best written as a generator to yield such numbers. The body of this generator consists of two nested loops. The outer loop iterates through the number of digits d in the current number.…Sevens rule, zeros drool def seven_zero(n): Seven is considered a lucky number in Western cultures, whereas zero is what nobody wants to be. Let us briefly bring these two opposites together by looking at positive integers that consist of some solid sequence of sevens, followed by some (possibly empty) solid sequence of zeros. Examples integers of this form are 7, 77777, 7700000, 77777700, and 70000000000000. A surprising theorem proves that for any positive integer n, there exist infinitely many integers of such seven- zero form that are divisible by n. This function should return the smallest such seven-zero integer. Even though discrete math and number theory help, this exercise is not about coming up with a clever symbolic formula and the proof of its correctness. This is rather about iterating through the numbers of this constrained form of sevens and zeros efficiently and correctly in strictly ascending order, so that the function can mechanistically find the smallest working…7. DIY Pattern by CodeChum Admin Step right up and create the patterni Whoever gets all patterns right willbe crowned the new King of Petterns and gets to brag about it to their friends. Here are the instructions: you will be given 4 numbers; each number corresponds to the amount of times a symbol is repested in the pattern. That's pretty much it. Good lack Symbels: nl n2 -1 n3 =/ n4. input 1. Value of nt Constraints The value is >- n3 2. Valua of n2 Constraints The value is greater than 0. 3. Value of na
- Leap Year: The earth doesn't take exactly 365 days to revolve around the sun and because of this we have leap years roughly every 4 years to make up the difference. The exact rule is: • Years divisible by 4 are leap years • except if they are also divisible by 100 and then they are not leap years (so 1900 was not a leap year), • unless they are also divisible by 400 and then they ARE leap years (so 2000 was a leap year). Part 1) Write a function in Python that takes as input a number, the year, and determines if it is a leap year or not. The function should return True if it is a leap year and False otherwise. Part 2) Write a main function to test out your leap year function on a few different illustrative inputs.Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. Write a code to check whether a entered number is a perfect number or not.Language: C Pascal’s triangle is a triangular array, useful for calculating the binomial coefficients, n k , that are used in expanding binomials raised to powers, combinatorics and probability theory. 0 0 1 0 1 1 2 0 2 1 2 2 3 0 3 1 3 2 3 3 4 0 4 1 4 2 4 3 4 4 Evaluating the values of the binomial coefficients, you get the following pattern, 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 The number of the entries in each row is increased by one, as we move down. Each number in the triangle, is constructed by adding the number above it and to the left, with the number above it and to the right. The blank entries as treated as 0. Using the recursion, implement the function that computes the Pascal’s triangle. Pr
- Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. Draw a flow chart of perfect number.hexadecimalWe usually write numbers in decimal form (or base 10),meaning numbers arecomposed using 10 different “digits” f0; 1; : : : ; 9g.Sometimes though it is useful to write numbers hexadecimal or base16. Now there are 16 distinct digits that can be used to form numbers:f0; 1; : : : ; 9;A; B; C;D; E; Fg. So for example, a 3 digit hexadecimalnumber might be 2B8.(a) How many 2-digit hexadecimals are there in which the first digitis E or F? Explain your answer in terms of the additive principle(using either events or sets).(b) Explain why your answer to the previous part is correct in termsof the multiplicative principle (using either events or sets). Whydo both the additive and multiplicative principles give you thesame answer?(c) How many 3-digit hexadecimals start with a letter (A-F) and endwith a numeral (0-9)? Explain.(d) How many 3-digit hexadecimals start with a letter (A-F) or endwith a numeral (0-9) (or both)? Explain.hexadecimal We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different “digits” {0, 1, . . . , 9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0,1,...,9,A,B,C,D,E,F}. So for example, a 3 digit hexadecimal number might be 2B8. (d) How many 3-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)? Explain (please answer it the way i can make myself understand)
- 1. Write an algorithm that asks the user to enter ten numbers and then prints the largest one.2. Write an algorithm that asks the user to enter a positive integer n and prints the sum of the divisors of n.Cyclops numbersdef is_cyclops(n):A nonnegative integer is said to be a cyclops number if it consists of an odd number of digits so that the middle (more poetically, the “eye”) digit is a zero, and all other digits of that number are nonzero. This function should determine whether its parameter integer n is a cyclops number, and return either True or False accordingly n Expected result 0 True 101 True 98053 True 777888999 False 1056 False 675409820 FalseC programming The field of astronomy has been significantly advanced through the use of computer technology. Algorithms can automatically survey digital images of the night sky, looking for new patterns. For this problem, you should write such an analysis program which counts the number of stars visible in an bitmap image. An image consists of pixels, and each pixel is either black or white (represented by the characters # and -, respectively). All black pixels are considered to be part of the sky, and each white pixel is considered to be part of a star. White pixels that are adjacent vertically or horizontally are part of the same star. Input Each test case begins with a line containing a pair of integers 1≤m, n≤100. This is followed by mm lines, each of which contains exactly nn pixels. Input contains at least one and at most 50 test cases, and input ends at the end of file. Output For each case, display the case number followed by the number of stars that are visible in the…