The function "decimal_to_IEEE754" is a Matlab function that converts a decimal number to its equivalent representation in the IEEE 754 format (double precision). It takes in one input, the decimal number to be converted, and returns the converted number as a string. The function first determines the sign bit of the number (0 for positive and 1 f…

decimal_to_IEEE754.m

function output = decimal_to_IEEE754(decimal)
    % Given a decimal number, this function returns the exact same number in
    % IEEE754 format (double precision)
    %   decimal: Decimal number to be converted
    %   output: Converted number (string)

    % Get the sign bit (0 for positive, 1 for negative)
    sign = 0;
    if decimal < 0
        sign = 1;
        decimal = abs(decimal);
    end

    % Get the exponent and mantissa
    [mantissa, exponent] = log2(decimal);
    mantissa = mantissa - 1;
    exponent = exponent + 1022;

    % Convert exponent and mantissa to binary
    exponent = dec2bin(exponent, 11);
    mantissa = dec2bin(round((mantissa - floor(mantissa)) * 2^53), 53);

    % Concatenate sign, exponent, and mantissa
    output = strcat(num2str(sign), " ", exponent, " ", mantissa(2:end));
end