Shortcut for Odd and Even number type questions

I have formulated a technique to solve type of 'Odd and Even number type questions' quickly, thus saving ample amount of time for other questions.
Basic concept used is of binary number calculations.

Binary Multiplication
0 * 0 = 0, 1 * 0 = 0, 1 * 0 = 0, 1 * 1 = 1

Binary Addition
0 + 0 = 0, 1 + 0 = 1, 0 + 1 = 1
1 + 1 = 10 or 0 [For applying the technique we need to consider last digit of ‘10’ i.e. ‘0’]

Application of Technique
Odd Number => 1
Even Numbers => 0

a. Odd Number * Odd Number = Odd number
1 * 1 = 1

b. Odd Number * Even Number = Even Number
1 * 0 = 0

c. Even Number * Even Number = Even Number
0 * 0 = 0

d. Odd Number + Odd Number = Even Number
1 + 1 = 0

e. Even Number + Odd Number = Odd Number
0 + 1 = 1

f. Even Number + Even Number = Even Number
0 + 0 = 0


Usage in Exam
Ex:

Solve (odd + (even * even * (odd + even) + odd * (even +even)) +even *odd) ?
Solution: (1 + ( 0 * 0 * ( 1 + 0 ) + 1 * ( 0 + 0 )) + 0 * 1 )
= (1 + ( 0 * 1 +0 ) + 0)
= (1 + 0 + 0)
= 1 =>(Odd)

This equation can be solved mentally within 15secs.
This technique has helped me in solving these types of question within 30 seconds with practice and hence saving a lot of time.