Which of the numbers with a 5bit unsigned binary representat

Which of the numbers with a 5-bit unsigned binary representation, i.e. numbers with a representation of the form b_4 b_3 b_2 b_1 b_0, are prime numbers? Recall that a number k is called a prime number if its only divisors are k and 1. Write the fully simplified Boolean expression for X Where X is high if the input b_4 b_3 b_2 b_1 b_0 corresponds to a prime number.

Solution

The Prime numbers are :

2,3,5,7,11,13,17,19,23,29,31

The Boolean expression is :

X = b4\'b3\'b2\'b1 + b0( ( b4\'( b2 xor b1) ) + ( b3\'( b4 xor b2) ) + ( b4( b3b2 + b3\'b1) ) )