Binary 11100 to Decimal Conversion Explained

This solution explains how to find the decimal equivalent of the binary number 11100. Binary is a base-2 number system, using only 0s and 1s, while decimal is base-10.

Understanding Binary to Decimal Conversion

To convert a binary number to its decimal equivalent, we multiply each digit of the binary number by the corresponding power of 2. We start from the rightmost digit, which corresponds to $2^0$, and move leftwards, increasing the power of 2 for each position.

Step-by-Step Conversion of 11100

The binary number is 11100. Let's break down the conversion:

• Identify the positions of each digit, starting from the right (position 0).
• The number 11100 has 5 digits.
• The powers of 2 corresponding to each position (from right to left) are $2^0$, $2^1$, $2^2$, $2^3$, and $2^4$.

We can represent the conversion as follows:

$$ 11100_2 = (1 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (0 \times 2^0) $$

Calculation Breakdown

Now, let's calculate the value for each position:

• Position 4 (leftmost): $1 \times 2^4 = 1 \times 16 = 16$
• Position 3: $1 \times 2^3 = 1 \times 8 = 8$
• Position 2: $1 \times 2^2 = 1 \times 4 = 4$
• Position 1: $0 \times 2^1 = 0 \times 2 = 0$
• Position 0 (rightmost): $0 \times 2^0 = 0 \times 1 = 0$

Summing these values gives the decimal equivalent:

$$ \text{Decimal Value} = 16 + 8 + 4 + 0 + 0 = 28 $$

Conversion Summary Table

Here is a table summarizing the process:

Conclusion

Therefore, the decimal equivalent of the binary number 11100 is 28.