Given the zhegalkin polynomial, find the boolean function

[Lilia]

Homework Statement

the given zhegalkin polynomial is y=x1+x2.
find the corresponding boolean functio

The Attempt at a Solution

zhegalkin polynomial for 2 variables is:
f(x) = c12*x1*x2 + c1*x1 + c2*x2 + c
=> c12=0, c1=1, c2=1, c=0.
therefore,
f(0,0) = c = 0,
f(0,1) = c2+c = 1+0 = 1
f(1,0) = c1+c = 1+0 = 1
f(1,1) = c1+c2+0 = 1+1+1 = 0
=> the boolean function should be xor?

y=x1 mod2sum x2 is in the answers but the answer chosen as correct
is y=x1 mod2sum x2 mod2sum x1x2. which one is correct?

p.s. mod2sum is "+ in circle"

 

[mighty2000]

Hello! Thank you for your question.

The correct boolean function for the given zhegalkin polynomial is y=x1 mod2sum x2 mod2sum x1x2.

The boolean function y=x1 mod2sum x2 is incorrect because it does not take into account the term x1x2 in the zhegalkin polynomial. This term is represented by the mod2sum operation in the correct boolean function.

Therefore, the correct boolean function should be y=x1 mod2sum x2 mod2sum x1x2, which takes into account all terms in the zhegalkin polynomial.

I hope this helps clarify any confusion. Let me know if you have any further questions. Good luck with your studies!