JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year STRUCTURED DIGITAL SYSTEM DESIGN Previous Question Paper (July/August - 2021 - R13)

To design a 1-bit magnitude comparator, let the two bits be A and B. We define three output functions: G (A > B), E (A = B), and L (A < B). The truth table is as follows:

From the truth table, the Boolean expressions are:

To use this as a module for an 8-bit comparator, the circuit must accept inputs from a less significant stage. Let G_in, E_in, and L_in be the outputs from the previous bit comparison. The modified logic for cascading is:

For the least significant bit, G_in = 0, L_in = 0, and E_in = 1.

Logic operators are fundamental building blocks of digital systems used to perform Boolean operations on binary variables:

• AND (Conjunction): Produces a high output (1) only if all input variables are high. Represented by the dot operator (A ⋅ B).
• OR (Disjunction): Produces a high output if at least one input variable is high. Represented by the plus operator (A + B).
• NOT (Inversion/Complement): A unary operator that inverts the input state (0 becomes 1, 1 becomes 0). Represented by a prime (A') or overbar.
• NAND: The complement of the AND operation; produces 0 only when all inputs are 1.
• NOR: The complement of the OR operation; produces 1 only when all inputs are 0.
• XOR (Exclusive OR): Produces 1 if the inputs are different. Represented by the circled plus operator (A ⊕ B).
• XNOR (Exclusive NOR): The complement of XOR; produces 1 if the inputs are identical.