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To simplify the Boolean expression ( abc' + ab'c' + a'bc' + a'b'c ), you can use the consensus and absorption laws. First, factor out common terms:
- From ( abc' + ab'c' ), factor out ( ac' ): ( ac' (b + b') = ac' ).
- From ( a'bc' + a'b'c ), factor out ( a'c ): ( a'c(b + b') = a'c ).
Now the expression becomes ( ac' + a'c ). This can be further simplified using the consensus theorem, but it is already in a simpler form. Thus, the simplified expression is ( ac' + a'c ).
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How would you simplify the boolean algebra expression a'bc plus ab'c plus abc' plus abc?
ab'c + abc' + abc = a(b'c + bc' + bc) = a(b'c + b(c' + c)) = a(b'c + b) = a(c + b) I'm not sure if there's a proper name for that last step, or multiple steps to get to it, but it is intuitively correct. b + b'c is equivalent to b + c. Here's a quick truth table to show it: bcb'b'cb'c+bb+c0010000111111000111100 11
What is he Boolean expression for 3 input XOR gate?
Out= A'B'C+AB'C'+AC'A'+ABC
Use Boolean algebra to simplify the logic function and realize the given function and minimized function using discrete gates. f equals ab c plus abc plus ac plus bc plus abC.?
Do you mean F = abc + abc + ac + bc + abc' ? *x+x = x F = abc + ac + bc + abc' *Rearranging F = abc + abc' + ab + bc *Factoring out ab F = ab(c+c') + ab + bc *x+x' = 1 F = ab + ab + bc *x+x = x F = bc
Simplify boolean algebra equation abc plus a'b'c' plus a'b'c plus a'bc plus ab'c' plus abc'?
In this case you want to group the terms so they have at least two terms in common. First step group and rewrite it: abc + a'bc + a'b'c' + a'b'c + ab'c' + abc' = Use the rule Identities x(y+z)=xy+xz: bc(a+a') + a'b'(c'+c) + ac'(b'+b) = Use the rule Identities x+x'=1: bc (1) + a'b'(1) + ac'(1) = Use the rule Identities x(1) = x: bc+a'b'+ac'
What is the boolean expression for a 2 out of 3 OR gate?
If the inputs are ABC. The inputs required to give an output are ABC, AB, AC and BC. Using the Absorption law X + X.Y = X we can remove ABC, the inputs required are therefore AB, AC and BC.
What is the truth table and the boolean expression of the following condition x is a 0 if any two of the three variables are 1?
The Truth Table would be: abc x 000 0 001 0 010 0 011 1 100 0 101 1 110 1 111 0 (or 1) (if you meant all 3 is also x=1) The Boolean expression is A'BC+AB'C+ABC' or if all three is x=1 just, AB+AC+BC
If a plus b plus c15 what is abc?
The expression "a plus b plus c" seems incomplete or unclear without additional context or equations. If you're asking about a scenario where ( a + b + c = 15 ), then to find ( abc ), we would need specific values for ( a ), ( b ), and ( c ). Without those values or further information, it's impossible to calculate ( abc ). Please provide more details for a precise answer.
How do you simlify variable algebraic expression with exponent?
Here are some rules that can help you simplify such expressions, in some cases. (ab)c=abc abac = ab+c ab/ac = ab-c
What steps were applied to abc to obtain a'b'c?
To obtain ( a'b'c ) from ( abc ), the steps typically involve applying logical operations such as negation and conjunction. First, each variable ( a ), ( b ), and ( c ) is negated, resulting in ( a' ), ( b' ), and ( c' ). Then, these negated variables are combined using conjunction (AND operation) to form the expression ( a'b'c ). This transformation is often used in Boolean algebra and digital logic design.
Is this an expression or an equation abc?
The phrase "abc" is neither an expression nor an equation; it is simply a sequence of letters. An expression typically consists of numbers, variables, and operations but does not contain an equality sign. An equation, on the other hand, includes an equality sign and states that two expressions are equal. Therefore, "abc" does not fit either category.
Aab plus BBC plus acc equals abc?
No.
ABC plus ABC equals CDD then what does ABC equals in numbers?
Assuming A, B, C and D all represent different digits then ABC = 183 .
