Introduction

Almost every modern electronic system — a calculator, a mobile phone, a computer, a digital watch — works internally not with smoothly varying voltages but with just two levels, usually written as 1 (HIGH) and 0 (LOW). Circuits that process information in this two-level form are called digital circuits, and this chapter of Karnataka 2nd PUC Electronics studies how they are built and simplified.

The building blocks of every digital system are logic gates, tiny circuits that follow the rules of Boolean algebra to produce an output from one or more binary inputs. From a handful of gates we can build circuits that add and subtract numbers, store a single bit, count, and take decisions. Before a computer can work with letters, digits and symbols, that information must also be turned into groups of bits using digital codes.

This chapter builds the subject up in stages. Section 10.1 introduces the logic gates — including the combinational XOR/XNOR gates and the universal NAND and NOR gates. Section 10.2 covers the digital codes (BCD, Excess-3, 2-4-2-1, Gray code and the alphanumeric ASCII/EBCDIC codes). Section 10.3 shows how gates combine into arithmetic logic circuits (half adder, half subtractor and full adder), and Section 10.4 explains how a Boolean expression is written and simplified using SOP/POS forms and the Karnaugh map so that a circuit uses the fewest gates. Later sections go on to sequential logic and flip-flops.

Digital Electronics is a scoring, logic-driven part of the II PUC board exam, and the ideas here — truth tables, gate realizations, code conversions and K-map minimisation — recur throughout the paper, so it rewards careful, step-by-step practice.