CS-Lab Assignment 1 Solution

Description

Assume that only the NOT gate, and the 2-input AND, OR and NAND gates are available.

1. Consider the following Boolean function:

( , , , ) = ∑ (1, 3,4,7,8,10,11) + ∑ (6,12,13,14,15)

Derive the minimal sum-of-products (MSOP) expression for F, and design the logic gate circuit for F using (a) AND, OR and NOT gates, and (b) NAND gates only. Test the circuit for all combinations of input variables.

2. 4-to-2 bit encoder: Inputs (1000, 0100, 0010, 0001) with expected outputs as (00, 01, 10, 11) respectively

2. 4-to-2 bit priority encoder: Inputs (1xxx, 01xx, 001x, 0001) with expected outputs as (00, 01, 10, 11) respectively. x can be 0 or 1.

2. 2-to-4 bit decoder: Inputs (00, 01, 10, 11) with expected outputs as (1000, 0100, 0010, 0001) respectively

2. 3-to-8 bit decoder: Inputs (000, 001, 010, 011, 100, 101, 110, 111) with expected outputs as (10000000, 01000000, 00100000, 00010000, 00001000, 00000100, 00000010, 00000001) respectively.