Converting Binary 11111111 to Decimal- Unveiling the Corresponding Decimal Number

What decimal number corresponds to the binary number 11111111? This is a common question among those who are learning about binary numbers and their conversion to decimal. In this article, we will explore the conversion process and provide a clear explanation of how the binary number 11111111 is equivalent to a specific decimal value.

Binary numbers are a base-2 numeral system that uses only two digits: 0 and 1. Each digit in a binary number is called a bit, and the position of each bit represents a power of 2. The rightmost bit is the least significant bit (LSB), and the leftmost bit is the most significant bit (MSB). The decimal number that corresponds to a binary number is obtained by summing the values of each bit, where the value of each bit is 2 raised to the power of its position.

To convert the binary number 11111111 to decimal, we can follow these steps:

1. Write down the binary number: 11111111
2. Starting from the rightmost bit, assign a power of 2 to each bit, starting with 2^0 for the LSB and increasing by 1 for each subsequent bit to the left.
3. Multiply each bit by its corresponding power of 2.
4. Sum the results of step 3 to obtain the decimal equivalent.

Applying these steps to the binary number 11111111:

1. Binary number: 11111111
2. Powers of 2: 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7
3. Multiply each bit by its corresponding power of 2:
– 1 2^0 = 1
– 1 2^1 = 2
– 1 2^2 = 4
– 1 2^3 = 8
– 1 2^4 = 16
– 1 2^5 = 32
– 1 2^6 = 64
– 1 2^7 = 128
4. Sum the results: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255

Therefore, the decimal number that corresponds to the binary number 11111111 is 255. This conversion is a fundamental concept in computer science and digital electronics, as it allows for the representation and manipulation of data in various systems.