Transitioning from Binary to Decimal: Conversion Basics
August 25, 2023 by JoyAnswer.org, Category : Mathematics
How do you convert binary to decimal?Discover the fundamental process of converting binary numbers to decimal. Learn about the underlying principles and mathematical calculations involved in this conversion.
How do you convert binary to decimal?
Converting binary numbers to decimal involves understanding the positional notation of both systems. In binary, each digit (bit) represents a power of 2, and in decimal, each digit represents a power of 10. The steps below outline how to convert a binary number to decimal:
Write Down the Binary Number: Start by writing down the binary number you want to convert to decimal.
Assign Positions: Assign a position to each bit in the binary number, starting from the right and increasing by 1 for each position. The rightmost bit is in position 0, the next to the left is in position 1, and so on.
Calculate Decimal Equivalent: For each bit in the binary number, multiply it by 2 raised to the power of its position and sum up these values.
Example: Convert the binary number 1101 to decimal.
- 1 * 2^3 = 1 * 8 = 8
- 1 * 2^2 = 1 * 4 = 4
- 0 * 2^1 = 0 * 2 = 0
- 1 * 2^0 = 1 * 1 = 1
Add Up the Results: Add up the values obtained in the previous step to get the decimal equivalent of the binary number.
In the example: 8 + 4 + 0 + 1 = 13
So, the binary number 1101 is equivalent to the decimal number 13.
Here's a general formula to help you convert binary to decimal:
Decimal = (bn * 2^n) + (bn-1 * 2^(n-1)) + ... + (b1 * 2^1) + (b0 * 2^0)
Where:
- bn, bn-1, ..., b1, b0 are the binary digits (bits) at each position.
- n is the position of the bit, starting from 0 for the rightmost bit.
You can use this process to convert any binary number to its decimal equivalent.
