Introduction
Boolean algebra is the mathematics of two values — 0 and 1 (also read as false/true or low/high). Every digital device — a CPU, a calculator, a router, a memory chip — is built from tiny switches that are either OFF (0) or ON (1). Boolean algebra gives us the rules for combining these two values, and logic gates are the physical (electronic) circuits that carry out those rules.
For the exam this is one of the highest-yield chapters in Digital Logic Design. BCS, Bank IT, and IT-officer papers repeatedly ask: the truth table of a gate, the number of NAND gates needed to build something, simplification using Boolean laws or K-maps, De Morgan's theorems, and "which gate is universal". Master this chapter and you can answer nearly every digital-logic MCQ quickly and correctly.
Learning objectives
- Define Boolean variables, constants, and the three basic operations (AND, OR, NOT).
- State and use the postulates and theorems of Boolean algebra, including De Morgan's theorems.
- Draw and recall the truth tables and symbols of all seven gates: AND, OR, NOT, NAND, NOR, XOR, XNOR.
- Explain why NAND and NOR are "universal" gates and build other gates from them.
- Simplify Boolean expressions using algebraic laws and Karnaugh maps (K-maps).
- Convert between an expression, a truth table, and a logic circuit; understand SOP and POS forms.
- Avoid the standard exam traps (precedence, De Morgan, XOR vs OR).