Question

Consider the following Boolean function: F(A,B,C,D)=∑m(7,10,11,13)+∑d

​(0,5,6,14,15) (d: don’t care)
1. Using K-map give the minimal SOP (sum of product) of F
2. Give the minimal SOP function using a 4:1 Mux
3. Give the minimal SOP function using NAND gates only.
4. If the propagation delay through a 2-input NAND gate is 4 ns and through a 3-input NAND gate is 5 ns, what is the maximum propagation delay and minimal propagation delay of the minimal SOP of F.

Answer 1

The student's question is about minimizing a Boolean function given as a sum of minterms with don't care conditions using a K-map, implementing it in a 4:1 MUX, and using NAND gates only, and calculating the propagation delays of the SOP function.

Step-by-step explanation:

The student is working on a Boolean function minimization problem which involves creating a simplified Sum of Products (SOP) expression for a given function F. This function F(A, B, C, D) is represented through a Karnaugh map (K-map) and is provided with specific minterms and don't care conditions, where the goal is to determine the minimal SOP. Additionally, they seek an implementation using a 4:1 multiplexer (MUX) and further wish to create a minimal SOP using only NAND gates.

The maximum and minimal propagation delays for the minimal SOP configuration using NAND gates is also requested, which requires analyzing the gate-level implementation to determine the longest and shortest paths that an input signal can take through the network of NAND gates.