Question

In: Computer Science

Simplify the equation using Boolean algebra properties. F = xy + xy’z + x’yz

Simplify the equation using Boolean algebra properties.

F = xy + xy’z + x’yz

Solutions

Expert Solution

F = xy + xy'z + x'yz
= xy(z+z') + xy'z + x'yz
= xyz + xyz' + xy'z + x'yz
= (xyz + xyz + xyz) + xyz' + xy'z + x'yz
= (xyz + xyz') + (xyz + xy'z) + (xyz + x'yz)
= (xy(z+z')) + (xz(y+y')) + (yz(x+x'))
= (xy(1)) + (xz(1)) + (yz(1))
= xy + xz + yz
Answer: xy + xz + yz

venereology answered 2 years ago
Next > < Previous

Related Solutions

3. Simplify the following expressions using the properties of boolean algebra : 3A)    S(A,B,C) = A'B'C...
3. Simplify the following expressions using the properties of boolean algebra : 3A)    S(A,B,C) = A'B'C + A'BC + AB'C + ABC 3B) F(A,B,C) = A'B'C' + A'B'C + AB'C' + AB'C + ABC' + ABC
Simplify the following Boolean expressions to the minimum number of terms using the properties of Boolean...
Simplify the following Boolean expressions to the minimum number of terms using the properties of Boolean algebra (show your work and write the property you are applying). State if they cannot be simplified A. X’Y + XY B. (X + Y)(X + Y’) C. (A’ + B’) (A + B)’ D. ABC + A’B + A’BC’ E. XY + X(WZ + WZ’)
Simplify the following Boolean expressions to the minimum number of terms using the properties of Boolean...
Simplify the following Boolean expressions to the minimum number of terms using the properties of Boolean algebra (show your work and write the property you are applying). State if they cannot be simplified. A. A’B + AB B. XY + X(WZ + WZ’) C. X’Y’(X’+Y)(Y’+Y) D. ABC + A’B + A’BC’ E. (A+B)(AC+AC’)+AB+B Draw the circuit logic diagrams for both the original and simplified expressions.
1. Use Boolean algebra to simplify the following Boolean expressions to expressions containing a minimum number...
1. Use Boolean algebra to simplify the following Boolean expressions to expressions containing a minimum number of literals: (a) A’C’ + A’BC + B’C (b) (A + B + C)’(ABC)’ (c) ABC’ + AC (d) A’B’D + A’C’D + BD (e) (A’ + B)’(A’ + C’)’(AB’C)’ (f) (AE + A’B’)(C’D’ + CD) + (AC)’ 2. Obtain the truth table of the function F = (AB + C)(B + AC), express the function F in sum-of-minterms and product-of-maxterms forms, and express...
1. Simplify the following expressions using Boolean algebra. a.A+AB b.AB+AB' c.A'BC+AC d.A'B+ABC'+ABC
1. Simplify the following expressions using Boolean algebra. a.A+AB b.AB+AB' c.A'BC+AC d.A'B+ABC'+ABC
For the Boolean function F = x + yz’+ x’z Show the truth table. Simplify F...
For the Boolean function F = x + yz’+ x’z Show the truth table. Simplify F by using k-map as SoP form.
Digital Logic Design Lab Prove the following Boolean Algebra theorems and properties by constructing Logic Circuits...
Digital Logic Design Lab Prove the following Boolean Algebra theorems and properties by constructing Logic Circuits for each theorem/properties using our educational simulation software: Q1-a) The Distributive Property:     a + ( b . c ) = ( a + b ) . ( a + c ) Q1-b) The Distributive Property:     a . ( b + c ) = ( a . b ) + ( a . c )
Assume B is a Boolean Algebra. Prove the following statement using only the axioms for a...
Assume B is a Boolean Algebra. Prove the following statement using only the axioms for a Boolean Algebra properties of a Boolean Algebra. Uniqueness of 0: There is only one element of B that is an identity for + please include all the steps.
computer organazation , Boolean algebra1. Show the Boolean algebra reduction to minimal form for each....
computer organazation , Boolean algebra1. Show the Boolean algebra reduction to minimal form for each. Show each step, and cite the rule number which allows it.a . (AB)’ (A’ + B) (B’ + B)b . A’(A+B) + (B + A)(A + B’)
How do you start an analysis and simplification using Boolean Algebra? Give a strategy for beginning...
How do you start an analysis and simplification using Boolean Algebra? Give a strategy for beginning such a problem.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT