Draw K-map using following
F(x, y, z) = xyz + xyz + xyz
Answers
Answer:
1. Create the Kmaps and then simplify the following functions:
a. F(x,y,z) = x'y'z' + x'yz + x'yz'
b. F(x,y,z) = x'y'z' + x'yz' + xy'z' + xyz'
2. Given the Boolean function: F(x,y,z) = x'y + xyz'
a. Derive an algebraic expression for the complement of F. Express in sum-of-products form.
b. Show that FF' = 0.
c. Show that F + F' = 1.
3. Draw the combinational circuit that directly implements the boolean expressions:
F(x,y,z) = xz + (xy+z')
4. Construct the XOR operator using only AND, OR, and NOT gates.
Karnaugh Map:
A Karnaugh Map or a K-map is a graphical technique that can be used to simplify complex Boolean functions in sum-of-products (SOP) or products-of-sum (POS) form. The Boolean function is first expanded to its canonical form, to get all the min-terms for SOP form (or max-terms for POS form). The min-terms are then placed in a map consisting of rows and columns, such that any two adjacent terms differ by just one bit and can hence be grouped together to eliminate a variable. A group of two min-terms will eliminate one variable, a group of four min-terms will eliminate two variables and so on. This grouping based variable elimination helps in simplifying the Boolean function.
Answer and Explanation:
1. a. F(x,y,z) = x'y'z' + x'yz + x'yz'
b. F(x,y,z) = x'y'z' + x'yz' + xy'z' + xyz'
The Kmaps and their simplified functions are as follows:
a.
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