Question

Build a digital circuit that can add two binary numbers of two bit each and shows the answer using three LEDs

1. Find the canonical equations of the following characteristics table in SOP and POS

2. Convert them and implement the SOP canonical equation only.

3. Simplify each equation SOP and POS and implement each one using logic gates.

4. Convert each circuit into its respective NAND-NAND and NOR_NOR and implement them using logic gates.

Objetivo: Construir un circuito digital que pueda Sumar dos números binarios de dos(2) bit cada uno y mostrarlo la repuesta a través de tres(3) led I. Encuentre las ecuaciones canónicas de la siguiente tabla características en su forma SOP y POS II.Convierta e implemente la ecuación SOP Canónico (solamente) III. Simplifique cada una de las ecuaciones tanto SOP como POS e implemente cada una usando compuertas lógicas Convierta cada circuito respectivamente en su forma Nand-Nand y Nor-Nor e implemente con compuertas Lógicas.| IV. Tabla 0 0 0 10 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 11 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 01 0 0 1 0 1 11 0 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 1 01 0 1

Answer 1

C_0 = sigma (10, 11, 13, 14, 15) S_1 = sigma (2, 3, 5, 6, 8, 9, 12, 15) S_0 = sigma (1, 3, 4, 6, 9, 11, 12, 14) K' maps: - C_0 = A_1B_1 + A_1 A_0 B_0 S_1 = A_1 B_1^bar B_0^bar + A_1 A_0^bar B_1^bar + A_1^bar A_0^bar B_1 + A_1^bar B_1 B_0^bar + A_1^bar A_0 B_1^bar + A_1 A_0 B_1 B_0 S_0 = A_0^bar B_0 + A_0 B_1^bar B_0^bar + A_1^bar B_! B_0 + A_1 A_0 B_1 B_0^bar For NAND-NAND implementation C_0 = A_1B_1 + A_1A_0B_0^barbar = (A_1 B_1)^bar (A_1A_0B_0)^bar S_1 = (A_1 B_1^bar B_0^bar)^bar (A_1 A_0^bar B_1^bar)^bar (A_1^bar A_0^bar B_1)^bar (A_1^bar B_1 B_0^bar)^bar (A_1^bar A_0 B_1^bar B_0)^bar (A_1 A_0 B_1 B_0)^bar S_1 = (A_1^bar B_0^bar) (A_0 B_1^bar B_0)^bar (A_1 A_0 B_1^bar B_0^bar)^bar NOR -NOR implementation: - C_0 = (A_^bar^bar) (B_1 + B_0)(A_0 + B_1) S_0 = (A_0 + B_0) (A_1 + B_1^bar + B_0) (A_0^bar + B_1 + B_0^bar)