Design a function F (A, B, C, D) to detect whether a number is a prime or not. The function has an output value of 1 if the input is not a prime number. The output is 0 otherwise. The simplified function is Select one: a. ABD + ABC + BCD + BCD b. ABC + AD + BD + BC + CD c. ABD + ABC + BCD + BCD d. ABC + AD + BD + BC + CD General Computer Organization (1)
b. ABC + AD + BD + BC + CD
To design a function that detects whether a number is prime or not, we need to go through the steps involved in determining primality. Here's one possible approach:
1. Initialize a variable, let's call it "isPrime," to 1 (indicating the number is not prime).
- This variable will be used to keep track of whether the number is prime or not. We assume that the number is not prime initially.
2. Check if the input number (let's call it "n") is less than 2. If it is, set "isPrime" to 1 and skip to the last step.
- Prime numbers are defined as positive integers greater than 1. Any number less than 2 cannot be prime.
3. Loop through all numbers from 2 to the square root of n.
- The goal of this loop is to check whether there is any number that evenly divides n, which would mean n is not prime.
4. Inside the loop, check if n is divisible by the current number. If it is, set "isPrime" to 1 and break out of the loop.
- If n is divisible by any number between 2 and the square root of n, then we can conclude that n is not a prime number.
5. After the loop, check the value of "isPrime." If it is still 0, set it to 0 (indicating n is prime).
- If the value of "isPrime" remains 1, it means the number did not have any divisors between 2 and the square root of n, therefore n is prime.
6. Return the value of "isPrime" as the output of the function.
Given the available options, the simplified function that matches the steps described above is option b. The function can be represented as:
F(A, B, C, D) = ABC + AD + BD + BC + CD