BCA Semester 1 – Digital Logic – Unit 3: Combinational Logic Design

Given: \( f(A,B,C,D) = \Pi(0,1,3,7,8,12) \) with don’t-care \( d(5,10,13,14) \) --- Key idea – how to handle don’t-care in K-map - Don’t-care cells (d) can be treated as either 1 or 0 — whiche

Definition of Decoder A decoder is a combinational logic circuit that takes an n-bit binary input and produces up to 2ⁿ output lines, such that for each input combination exactly one output is activ

Definition: Read‑Only Memory (ROM) - ROM is a non‑volatile memory that stores fixed binary data (0s and 1s) which cannot be (easily) changed during normal operation. - Internally, a ROM has k add

1. Definition of PLA PLA (Programmable Logic Array) is a combinational logic device used to implement multiple Boolean functions. - It consists of two levels of logic: 1. Programmable AND plane

1. Definition of Universal Gate A universal gate is a logic gate that can be used to implement any Boolean function (AND, OR, NOT, etc.) without using any other gate. - NAND and NOR are universal ga

1. Definition of Decoder A decoder is a combinational circuit that converts n input lines into 2ⁿ unique output lines. - Each output corresponds to one combination of input values. - Used in memor

1. Given Function \[ F(w, x, y, z) = \prod M(0,2,4,6,8,10,12,14) \] Don't care conditions: \[ d(w, x, y, z) = \prod M(1,3,9,11) \] > Note: π represents product of maxterms (POS form). --- 2. St

1. Definition of Multiplexer A Multiplexer (MUX) is a combinational circuit that selects one of many inputs and sends it to a single output line based on select lines. - Also called a data selector.

1. Given Function \[ F(A, B, C, D) = \prod M(2, 3, 4, 5, 7, 9, 10) \] Don't care conditions: \[ d(A, B, C, D) = \prod M(0, 6, 11) \] > π denotes product of maxterms (POS form). --- 2. Step 1: C

1. Definition: Combinational Logic Circuit - A Combinational Logic Circuit is a type of digital circuit where output depends only on the current input values, not on past inputs (no memory). - Chara

1. Definition of Decoder - A Decoder is a combinational circuit that converts n input lines into a maximum of 2ⁿ unique outputs, with only one output active at a time. - Purpose: To decode a binary

1. Basic Logic Gates | Gate | Symbol | Function | Boolean Expression | Truth Table | |------|--------|---------|-----------------|-------------| | AND | A⋅B | Output is 1 if both inputs are 1 | F = A⋅

1. Programmable Logic Array (PLA) - Definition: A PLA is a programmable device used to implement combinational logic circuits. It consists of a programmable AND plane and a programmable OR plane.

1. Definition - A Multiplexer (MUX) is a combinational circuit that selects one input from many inputs and sends it to a single output line based on select lines. - Function: Data selector. - Appl

Given Function - F(A, B, C, D) = Π(0, 1, 3, 7, 8, 12) - Don't care conditions: d(A, B, C, D) = Π(5, 10, 13, 14) We are to find SOP and POS forms. --- Step 1: Construct K-Map (4-variable) | AB\CD

1. Definition of Combinational Circuit - A combinational circuit is a logic circuit whose output depends only on the current inputs. - No memory elements or feedback are used. - Examples: Adders,

4:2 Priority Encoder — Corrected Answer Definition A priority encoder encodes the index of the highest-priority active input among many inputs. For a 4:2 priority encoder inputs are I3 (highest), I2,

Definition A universal gate is a logic gate that can be used to implement any Boolean function using only that type of gate. Reason NAND and NOR gates are called universal gates because: - Any basic

1. Definition: PLA - PLA (Programmable Logic Array) is a combinational logic device used to implement multiple Boolean functions. - Features: - Programmable AND plane (for product terms / minterms)

1. Universal Gates Universal gates can be used to implement any Boolean function (AND, OR, NOT, etc.). a) NAND Gate Logic Expression: \[ F = \overline{A \cdot B} \] Truth Table: | A | B | F = A NAN