A number in base 2 (binary) is a number such that each of its digits is 0 or 1. To convert from binary to decimal (base 10), the digits starting from the right are multiplied by powers of 2 (starting at 0) and added. For example, the value in decimal of 10011 is calculated as follows:
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A number in base 2 (binary) is a number such that each of its digits is 0 or 1. To convert from
binary to decimal (base 10), the digits starting from the right are multiplied by powers of 2
(starting at 0) and added. For example, the value in decimal of 10011 is calculated as follows:
Step by step
Solved in 2 steps
- On the planet Tatooine, droids do computations in base-6. What is the greatest base-6 number with three different digits? (Your base-6 number must have a separate digit for each digit.) Make a decimal out of your answer (base-10).In the example below, the sum of the fourth powers of each digit that forms the 4-digit numbers gives the number itself: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 And sum of these numbers is 1634 + 8208 + 9474 = 19316. Find the sum of all numbers that can be written as the sum of the fifth forces of their numbers. (P.s.: You have to done it by C++)On a piano, a key has a frequency, say f0. Each higher key (black or white) has a frequency of f0 * rn, where n is the distance (number of keys) from that key, and r is 2(1/12). Given an initial key frequency, output that frequency and the next 4 higher key frequencies. Output each floating-point value with two digits after the decimal point, which can be achieved as follows:print('%0.2f %0.2f %0.2f %0.2f %0.2f' % (your_value1, your_value2, your_value3, your_value4, your_value5))
- Suppose you save $100 each month in a savings account with annual interest rate 3.75%. Thus, the monthly interest rate is 0.0375/12 = 0.003125. After the first month, the value in the account becomes 100 * (1 + 0.003125) = 100.3125, after the second month, the value in the account becomes (100 + 100.3125) * (1 + 0.003125) = 200.938, after the third month, the value in the account becomes (100 + 200.938) * (1 + 0.003125) = 301.878 and so on. Write a Java program that prompts the user to enter a monthly saving amount and displays the account value after the sixth month. (You will use a loop to simplify the code and display the account value for any month.) Sample Output:Enter the monthly saving amount: 100After the first month, the account value is 100.3125After the second month, the account value is 200.9384765625After the third month, the account value is 301.8789093017578Note: The computation should be until 12 months.On a piano, a key has a frequency, say f0. Each higher key (black or white) has a frequency of f0 * rn, where n is the distance (number of keys) from that key, and r is 2(1/12). Given an initial key frequency, output that frequency and the next 4 higher key frequencies. Output each floating-point value with two digits after the decimal point, which can be achieved by executingcout << fixed << setprecision(2); once before all other cout statements.Our usual number system is base 10, because it strings together the digits 0 – 9 to form any whole number (there is a 1’s place, a 10’s place, a 10-squared’s place, etc). Hexadecimal numbers are written in base 16. This means they string together the digits 0 – 9 and the letters A – F to form any whole number (there is a 1’s place, a 16’s place, a 16-squared’s place, etc). For example, BD3C8 and 305A2 are two different 5-digit hexadecimal numbers. How many 9-digit hexadecimal numbers are there that have exactly 4 zeroes. (Note: Hexadecimal numbers, like our normal base 10 numbers, cannot start with a 0)
- In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, …a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime(int num) b. Write a Java class called PrimeNumbers that: o Reads from the user a natural value n (should be less than or equal 200). o Prints a list of the prime numbers from 2 to n and their number and values. o The program has to work EXACTLY as given in the following sample run.1.Given a positive integer, N, the ’3N+1’ sequence starting from N is defined as follows:If N is an even number, then divide N by two to get a new value for NIf N is an odd number, then multiply N by 3 and add 1 to get a new value for N.Continue to generate numbers in this way until N becomes equal to 1For example, starting from N = 3 the complete ’3N+1’ sequence would be:3, 10, 5, 16, 8, 4, 2, 1Write c++ code to ask the user to enter a positive integer (N) in the main() function. Write a function sequence()that receives the integer value N and display the ‘3N+1’ sequence starting from the integer value that wasreceived (entered by the user). The function must also count and return the numbers that the sequenceconsists of. The returned value must be displayed from the main() function.Write a program using Java programming language that reads one integer number and outputs (writes) the sum of all numbers that are lower or equal to this number and that are divisible by 5
- in the United States, telephone numbers consist of a three digit area code followed by a seven digit local number. Suppose neither the first digit of an area code nor the first digit of a local number can be a zero but that all other choices are acceptable. do not use commas when you write your number. For example enter 3356789 NOT 3,456,789A number in base 2 (binary) is a number such that each of its digits is 0 or 1. To convert frombinary to decimal (base 10), the digits starting from the right are multiplied by powers of 2(starting at 0) and added. For example, the value in decimal of 10011 is calculated as follows: 1 ×20+ 1 ×21+ 0 ×22+ 0 ×23+ 1 ×24=19 Write a program that reads from the user a 5-digit integer representing a value in binary anddisplays its equivalent value in decimal. Note that if the user enters an integer which digits areother than 0 or 1, the program displays a message stating that the number is not valid.On a piano, a key has a frequency, say f0. Each higher key (black or white) has a frequency of f0 * rn, where n is the distance (number of keys) from that key, and r is 2(1/12). Given an initial key frequency, output that frequency and the next 4 higher key frequencies. Output each floating-point value with two digits after the decimal point, which can be achieved by executingcout << fixed << setprecision(2); once before all other cout statements. Ex: If the input is: 440.0 (which is the A key near the middle of a piano keyboard), the output is: 440.00 466.16 493.88 523.25 554.37 Note: Use one statement to compute r = 2(1/12) using the pow function (remember to include the cmath library). Then use that r in subsequent statements that use the formula fn = f0 * rn with n being 1, 2, 3, and finally 4.