1. Digital Logic Gates
Logic gates are the physical building blocks of digital integrated circuits:
- AND Gate: Output is 1 only if ALL inputs are 1 (
F = A . B). - OR Gate: Output is 1 if AT LEAST ONE input is 1 (
F = A + B). - NOT Gate: Inverts the input (
F = A'orF = Ā). - XOR (Exclusive OR) Gate: Output is 1 if inputs are different (
F = A ⊕ B).
2. Universal Gates
NAND and NOR gates are classified as universal gates because any basic logic function (NOT, AND, OR) can be constructed solely using them.
Example: NOT gate using a NAND gate: Connect both inputs of a 2-input NAND gate together. When the input is A, the NAND output is (A . A)' = A', which acts as a NOT gate.
3. Karnaugh Map (K-Map) Simplification
A Karnaugh Map is a graphical method used to simplify Boolean expressions (SOP form) without using algebraic laws.
K-Map Rules:
- Use Gray Code ordering for the row/column coordinates (e.g.,
00, 01, 11, 10). This ensures only one bit changes between adjacent cells. - Group adjacent 1s in sizes of powers of 2 (pairs of 2, quads of 4, octets of 8).
- Make groups as large as possible to reduce variables, allowing overlapping of cells and wrapping around borders.
