Question

Answer the toliowing questons rerated to the tuncuon f(A,B,C,D) as oenneo by tis minterms: f(A,B,C,D)=∑m(7,9,11,12,13,14,15)

(a) Enter the minterms and maxterms on a suitable K-map and deduce the minimal 2ⁿᵗ canonical form for f(A,B,C,D).

Answer 1

The question is about using a Karnaugh map to simplify Boolean algebra expressions, specifically by placing minterms on the map and deducing a minimal expression for the given function f(A,B,C,D) using Boolean algebra.

Step-by-step explanation:

The student's question pertains to Karnaugh maps (K-maps), which are used to simplify Boolean algebra expressions. The function f(A,B,C,D) is given in terms of its minterms: f(A,B,C,D)=\u2211m(7,9,11,12,13,14,15). To find the minimal 2¹ canonical form, each minterm must be represented on the K-map. The K-map helps to visualize and combine adjacent terms, thereby reducing the overall complexity of the function.

Minterms correspond to the binary representations of the given indices with '1' in the function's output. Maxterms are not directly listed but are the complement of the minterms in this context. Simplifying the function with K-map involves grouping the 1s in the K-map that are powers of 2 (1, 2, 4, 8) to form the simplest possible expression. After placing minterms on the K-map, we look for the largest possible groupings of '1's that can be made, while ensuring each grouping is a rectangle of size 1, 2, 4, or 8, and contains a number of '1's that is a power of 2. These groupings help deduce the function in its minimal form by considering common variables within each group that can be combined using Boolean algebra. Once simplified, the resulting expression will be the 2¹ canonical form of the function.