Final answer:
To simplify the function F(x, y, z) using Kmaps, minterms are placed onto the 3-variable Kmap and groups of 1s are identified. This results in the simplified function F(x, y, z) = y'z' + yz', which is further reduced to F(x, y, z) = z'.
Step-by-step explanation:
Creating Kmaps and Simplifying the Function:
To simplify the function F(x, y, z) = x'y'z' + x'yz' + xy'z' + xyz' using Karnaugh maps (Kmaps), we begin by setting up a 3-variable Kmap. Each square of the Kmap corresponds to a combination of the variables x, y, and z. The expression can be mapped onto the Kmap by placing a 1 in the squares corresponding to the minterms of the function (where the function F is true). Here, the minterms are:
- x'y'z' (00-1)
- x'yz' (01-1)
- xy'z' (10-1)
- xyz' (11-1)
Once the Kmap is filled, we look for groups of 1s that can be combined to simplify the function. In this function, we can group the 1s horizontally, yielding two groups:
- The group of x'y'z' and xy'z', which simplifies to y'z'.
- The group of x'yz' and xyz', which simplifies to yz'.
Combining these two groups, the simplified function is F(x, y, z) = y'z' + yz'. We notice that z' is a common factor, so we can further simplify the equation to F(x, y, z) = z'.