📘 digital logic

1. **Stating the problem:** We need to solve for the function $$F_3 = \Sigma(2, 4, 6, 7)$$ where the variables are $A, B, C, D$.

1. **State the problem:** Construct the circuit for the Boolean expression $ (x+z)(y+z) $. 2. **Recall Boolean algebra rules:**

1. **State the problem:** Construct circuits for the Boolean expression $xyz + xyz$. 2. **Understand the expression:** The expression is $xyz + xyz$. Notice that $xyz$ and $xyz$ di

1. Problem: Simplify the Boolean expression $$Y = AB + \overline{A}C + BC$$. 2. Formula and rules: Use Boolean algebra simplification rules such as the Distributive Law, Consensus

1. **State the problem:** Simplify the Boolean expression $$F = AB\overline{B} + AC(AB)$$ and understand its logic gate representation. 2. **Recall Boolean algebra rules:**

1. **State the problem:** We are given the Boolean function $F = AC + AB$ and asked to deduce its Karnaugh map (K-map) and find the simplified expression. 2. **Identify variables:*

1. **Problem statement:** Given the Boolean function $F = AC + AB$, we want to deduce its Karnaugh map (K-map). 2. **Recall the variables and function:** The function depends on va

1. مسئله: صورت نرمال فصلی مینیمال عبارت $\overline{y}zt + xzy + \overline{x}y\overline{z}$ را بیابید. 2. ابتدا عبارت را بررسی می‌کنیم:

1. **Problem Statement:** We have three logic circuits (Questions 4, 5, and 6) involving NOT, AND, OR, and XOR gates. We need to find the Boolean expressions and truth tables for e

1. **Problem Statement:** We have a sequential circuit with four flip-flops A, B, C, D described by the state equations:

1. Simplify the function using De Morgan's Theorem: (M + N)(M + N) - The problem is to simplify the expression (M + N)(M + N).

1. **Problem a:** Find the largest decimal value that can be represented using 12 bits. 2. **Solution a:** The largest decimal number in binary with $n$ bits is when all bits are 1

1. The problem asks to draw circuit diagrams for three Boolean expressions without simplifying them. 2. Boolean expressions use variables (A, B, C) and operations: NOT (̅), AND, OR

1. The problem is to implement the Boolean expression $$y = AC + BC\overline{} + ABC\overline{}$$ as a logic circuit. 2. First, identify the variables and their complements: inputs

1. The problem is to express the function $$F(A,B,C) = AB' C' + AC + (B + C')$$ using logic gates and draw its circuit diagram. 2. First, simplify the function if possible.

1. **State the problem:** We have a logic circuit with inputs A, B, and C.

1. **State the problem:** We have two sensors, A and B, controlling a door. The door opens (output 1) if either sensor A is activated or both sensors A and B are activated. 2. **Co

1. The problem is to draw the logic circuit for the Boolean expression: $$ (xyz) + (x+y+z)' + (x'zy') $$

1. Problem 1: Determine which logic gate shows HIGH when both tanks are more than one-quarter full (sensors output 5 V at >25%). - Both sensors are HIGH (5 V) when tanks >25% full.

1. **State De Morgan's law.** De Morgan's laws are two transformation rules that are useful in Boolean algebra and set theory. They state:

1. **Problem statement:** Simplify the Boolean expression $\overline{A}B + \overline{A}\overline{B}\overline{C} + A\overline{B}\overline{C} + ABC$ and construct its circuit diagram