SISTEMA BINÁRIO | NÚMERO BINÁRIO EM DECIMAL | \Prof. Gis/

Introduction

This tutorial will guide you through the process of converting binary numbers to decimal. Understanding this conversion is essential in mathematics, computer science, and digital electronics. By the end of this tutorial, you will be able to confidently transform binary numbers into their decimal equivalents.

Step 1: Understanding Binary Numbers

• Definition: Binary numbers use only two digits, 0 and 1. Each digit represents a power of 2, starting from the rightmost digit which is 2^0.

Example: The binary number 10010 can be broken down as follows

• 1 × 2^4 (16)
• 0 × 2^3 (0)
• 0 × 2^2 (0)
• 1 × 2^1 (2)
• 0 × 2^0 (0)

Step 2: Converting Binary 10010 to Decimal

1. Write down the binary number: 10010.
2. Identify the position of each digit from right to left, starting at 0.

Multiply each digit by 2 raised to the power of its position

• 1 × 2^4 = 16
• 0 × 2^3 = 0
• 0 × 2^2 = 0
• 1 × 2^1 = 2
• 0 × 2^0 = 0

Sum the results

• 16 + 0 + 0 + 2 + 0 = 18
3. Therefore, the decimal equivalent of binary 10010 is 18.

Step 3: Using a Table for Conversion

• Create a table to organize the binary digits and their corresponding powers:

  | Binary Digit | Position | Power of 2 | Value |
  |--------------|----------|-------------|-------|
  | 1            | 4        | 16          | 16    |
  | 0            | 3        | 8           | 0     |
  | 0            | 2        | 4           | 0     |
  | 1            | 1        | 2           | 2     |
  | 0            | 0        | 1           | 0     |
  

• Sum the values from the table to get the decimal equivalent.

Step 4: Converting Binary 01011 to Decimal

1. Write down the binary number: 01011.

Assign positions and calculate

• 0 × 2^4 = 0
• 1 × 2^3 = 8
• 0 × 2^2 = 0
• 1 × 2^1 = 2
• 1 × 2^0 = 1

Sum the results

• 0 + 8 + 0 + 2 + 1 = 11
2. The decimal equivalent of binary 01011 is 11.

Step 5: Converting Binary 001101 to Decimal

1. Write down the binary number: 001101.

Calculate each position

• 0 × 2^5 = 0
• 0 × 2^4 = 0
• 1 × 2^3 = 8
• 1 × 2^2 = 4
• 0 × 2^1 = 0
• 1 × 2^0 = 1

Sum the results

• 0 + 0 + 8 + 4 + 0 + 1 = 13
2. The decimal equivalent of binary 001101 is 13.

Conclusion

You have learned how to convert binary numbers to decimal using both direct calculation and a tabular format. Practice with different binary numbers to strengthen your understanding. For further exploration, consider learning how to convert decimal numbers back to binary or exploring how binary is used in computing.