Math Problem Statement

Modul3.pdf

58.63 KB

AAkerjakan tugas

Solution

From the document you uploaded, I see that your task involves simplifying logic circuits using Boolean algebra rules. Here are the steps to complete the tasks mentioned in the document:

Task 1: Simplify the Expression

You are required to simplify the following Boolean expressions and build the circuit based on the simplified results, followed by constructing a truth table:

Expression 1:

X=A(A+B+C)X = A \cdot (A + B + C)

Solution:

  1. Apply Absorption Law (Rule 10): A(A+B)=AA \cdot (A + B) = A. X=AX = A The simplified expression for XX is AA.

  2. Truth Table:

    • If A=1A = 1, then X=1X = 1.
    • If A=0A = 0, then X=0X = 0.

Expression 2:

X=(AB)+(CDA)X = (A \cdot B) + (C \cdot D \cdot A)

Solution:

  1. Factor AA out from both terms: X=A(B+CD)X = A \cdot (B + C \cdot D)

This is the simplified expression.

  1. Truth Table: You can now construct the truth table based on the simplified form X=A(B+CD)X = A \cdot (B + C \cdot D).

Task 2: Simplify the Circuit in Figure 3-3

You are also tasked with simplifying a given circuit (refer to "Gambar 3-3"). Based on Boolean simplifications, simplify the logic gate arrangement and compare the truth tables before and after simplification.

Would you like detailed explanations or any help with circuit diagrams?


Here are 5 related questions that might help you expand your understanding:

  1. What is the role of De Morgan's laws in simplifying Boolean expressions?
  2. How does the truth table change when you simplify a logic circuit?
  3. Can every logic circuit be simplified using Boolean algebra?
  4. How would the circuit for Expression 2 change after simplification?
  5. What are the key differences between logic circuit simplifications before and after simplification?

Tip: Always apply the Absorption and Distribution rules when simplifying complex Boolean expressions.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Boolean Algebra
Logic Circuits
Simplification of Boolean Expressions

Formulas

Absorption Law: A ⋅ (A + B) = A
De Morgan's Theorems: (X + Y)' = X' ⋅ Y', (X ⋅ Y)' = X' + Y'
Distribution Law: X ⋅ (Y + Z) = (X ⋅ Y) + (X ⋅ Z)

Theorems

De Morgan's Theorem
Boolean Algebra Laws

Suitable Grade Level

College Level