simplify the following expression with the help of XOR and XNOR:
X = ABCD+A(~B)(~C)D+(~A)(~B)
~ means not e.g. ~B is not b
A nice calculator is here. An example is
https://www.wolframalpha.com/input/?i=((A+OR+B)+AND+(NOT+B+AND+C)+OR+C)&t=crmtb01&f=rc
thanks
To simplify the given expression using XOR (exclusive OR) and XNOR (exclusive NOR), we can apply some Boolean algebra simplification rules. The XOR operation returns true (1) if and only if the inputs are different. The XNOR operation returns true (1) if and only if the inputs are the same.
Let's simplify the given expression step by step:
1. Distribute the OR operation over the AND operation:
X = ABCD + A(~B)(~C)D + (~A)(~B)
2. Apply the De Morgan's law to eliminate the NOT (~) operators:
X = ABCD + A(B+C)D + (A+B)
3. Expand the middle term using the distributive property:
X = ABCD + AB(D+C)D + (A+B)
4. Apply the XOR and XNOR simplification rules:
- For the first term (ABCD), there are no other similar terms to simplify with.
- For the second term AB(D+C)D, we can distribute the D:
X = ABCD + ABD^2 + ACD^2 + (A+B)
5. Simplify the second term:
Since D^2 is equal to D, we have:
X = ABCD + ABD + ACD + (A+B)
6. Group similar terms:
X = ABCD + ABD + ACD + A + B
This is the simplified expression using XOR and XNOR: X = ABCD + ABD + ACD + A + B