Binary to Decimal Conversion Explained

To find the decimal equivalent of a binary number, we multiply each binary digit by the corresponding power of 2, starting from the rightmost digit (which corresponds to $2^0$). We then sum up all these products.

Converting (1011100)₂

The given binary number is $(1011100)_2$. Let's break down the conversion process step-by-step:

The binary number has 7 digits: $1, 0, 1, 1, 1, 0, 0$. We assign powers of 2 starting from 0 on the rightmost side.

The calculation is as follows:

$(1011100)_2 = (1 \times 2^6) + (0 \times 2^5) + (1 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (0 \times 2^0)$

Now, let's calculate the value of each term:

• $1 \times 2^6 = 1 \times 64 = 64$
• $0 \times 2^5 = 0 \times 32 = 0$
• $1 \times 2^4 = 1 \times 16 = 16$
• $1 \times 2^3 = 1 \times 8 = 8$
• $1 \times 2^2 = 1 \times 4 = 4$
• $0 \times 2^1 = 0 \times 2 = 0$
• $0 \times 2^0 = 0 \times 1 = 0$

Finally, sum up all the results:

$64 + 0 + 16 + 8 + 4 + 0 + 0 = 92$

Therefore, the decimal equivalent of $(1011100)_2$ is $(92)_{10}$.

Summary Table