MATLAB Implementation for Decimal and Binary Conversion with Code Examples

Implementing arbitrary decimal and binary conversions in MATLAB is a common numerical computation task. MATLAB provides built-in functions to handle such requirements while also supporting custom functions for more flexible conversion logic.

Decimal to Binary Conversion The built-in `dec2bin` function directly converts decimal integers to binary strings. This function accepts a decimal number as input and returns the corresponding binary representation. For floating-point numbers, you can separate the integer and fractional parts using the `fix` and `rem` functions, then combine their binary results using string concatenation. For example: % Convert decimal integer bin_str = dec2bin(10); % Returns '1010' % Convert floating-point number num = 13.625; int_part = fix(num); frac_part = num - int_part; int_bin = dec2bin(int_part); % Convert fractional part through iterative multiplication by 2

Binary to Decimal Conversion The `bin2dec` function converts binary strings to decimal integers. For binary numbers containing fractional parts, process integer and fractional sections separately using positional notation, then sum the results. The conversion algorithm involves: % Convert binary integer dec_val = bin2dec('1101'); % Returns 13 % Convert binary fraction bin_frac = '101'; frac_val = 0; for i = 1:length(bin_frac) frac_val = frac_val + str2double(bin_frac(i)) * 2^(-i); end

Custom Implementation For greater flexibility or larger numerical ranges, manual conversion algorithms can be implemented. The decimal-to-binary algorithm uses successive division by 2 while recording remainders in reverse order: function bin_str = custom_dec2bin(dec_num) bits = []; while dec_num > 0 bits = [mod(dec_num,2), bits]; dec_num = floor(dec_num/2); end bin_str = num2str(bits); end Binary-to-decimal conversion employs the positional notation method, multiplying each bit by its corresponding power of 2: function dec_num = custom_bin2dec(bin_str) dec_num = 0; for i = 1:length(bin_str) dec_num = dec_num*2 + str2double(bin_str(i)); end end

These MATLAB capabilities are particularly suitable for scientific computing and engineering applications, especially in scenarios requiring frequent handling of data in different numeral systems.