binarytodecimal

Binary to decimal refers to the process of converting a number written in base-2, using only the digits 0 and 1, into base-10, the decimal system. In binary, each digit represents a power of two, with the rightmost bit representing 2^0 and moving leftward to higher powers. The decimal value is obtained by summing the products of each bit and its corresponding power of two.

For positive integers, the conversion is straightforward: for example, 1011012 equals 32 + 0 + 8 + 4 + 0 + 1 = 45, so 1011012 = 45 in decimal.

For binary fractions, digits after the binary point represent negative powers of two. For instance, 0.1011_2 equals 1/2 + 0/4 + 1/8 + 1/16 = 0.6875 in decimal.

Negative numbers can be represented using two's complement in a fixed number of bits; to interpret, one must know the width. For example, in 8-bit two's complement, 11111101_2 equals -3. The magnitude is obtained by inverting the bits and adding 1, then applying a negative sign.

In practice, binary-to-decimal conversion is foundational in computing and digital electronics. It is supported by calculators, programming languages, and various software tools. Typical methods range from manual calculation using positional weights to built-in functions in programming languages, such as int('101101', 2) in Python, which returns 45.