Function for Converting Binary to Decimal with Algorithm Implementation

Implementing a binary-to-decimal conversion function in MATLAB requires handling multiple scenarios including integers, fractional numbers, and negative values. This conversion typically involves bitwise weight expansion and sign processing algorithms.

For fractional binary conversion, the binary string can be split into integer and fractional parts. Each bit in the integer part represents powers of 2 (2^0, 2^1, 2^2, etc.) from right to left, while the fractional part represents negative powers of 2 (2^-1, 2^-2, 2^-3, etc.) from left to right. The complete decimal value is obtained by calculating the sum of both parts separately and combining them. In code implementation, this involves using string manipulation functions like `split()` or `strtok()` to separate the parts, followed by iterative multiplication and accumulation using powers of 2.

For negative binary conversion, the most significant bit (leftmost bit) typically serves as the sign bit, where 0 indicates positive and 1 indicates negative. The algorithm first processes the sign bit, performs standard binary-to-decimal conversion on the remaining bits, and finally applies negation based on the sign bit. A practical implementation would check the first character using conditional statements like `if-else` and manipulate the substring accordingly.

While MATLAB's built-in `bin2dec` function works for positive integer conversions, custom functions are needed for complex binary formats (containing fractions or negatives). Such functions generally parse input strings to separate sign bits, integer parts, and fractional parts using regular expressions or string indexing, compute decimal equivalents through weighted summation loops, and combine results with proper sign handling. Key implementation steps include input validation, bit-by-bit processing with power-of-2 multipliers, and error checking for invalid characters.