# Convert signed decimal to binary matlab

After introducing floating point numbers and sharing a function to convert a floating point number to its binary representation in the first two posts of this series, I would like to provide a function that converts a binary string to a floating point number. I will convert between different types of binary representations and discuss their merits.

Conversion from a floating point binary representation to decimal can be performed with different several methods. The first method involves converting the significand and exponent to decimal, multiplying them, and then assigning the sign bit. Control statements for special numbers e. As I mentioned in the last past, this would be instructive but slow. The second method, demonstrated below, involves the use of typecast.

A call to bin2dec is performed on the binary string to convert it into a decimal format. A cast to a bit unsigned integer using uint64 is then performed, followed by a typecast to double. However, as the following example shows, this method does not preserve precision, and the least significant digits are lost.

In this example, the last 9 digits are lost, but the number of digits lost depends on the number. We recommend a third method that performs the steps of float2bin in reverse order, which is presented below.

The corresponding hex values 0 — f are obtained by accessing the locations of the hex array, and finally, the floating point decimal value is produced by utilizing hex2num.

The following example shows that this function preserves all of the digits of the binary representation. Depending on the application, it may be preferable to hold the binary representation of a floating point number in a certain data type. For this reason, we will now discuss conversions among binary logical vectors, numerical vectors, and character strings. Conversion from a character string is to a numerical vector is quite simple. In the interest of readability, float2bin outputs binary numbers in the form of a character string.

If it is necessary to perform calculations with the binary representation of a float, a numerical or logical format is preferable. Additionally, if there are tight constraints on memory usage in a program, it may be necessary to use a format other than a vector of doubles to store your bit vector. The commands presented below show how to convert between various types of bit vectors, including character strings, logical vectors, and various numerical vectors. As shown in the whos table, the various data types occupy different amounts of memory.

In order of increasing memory consumption, we have the original floating point number; the hexadecimal string; a tie at 64 bytes among the character string, the logical vector, and the int8 vector; the single vector; and the double vector. Thus, representing a number as a bit vector will always carry a memory cost of a factor of 8 to 64, and the most efficient way to store floating point data is in its original format, as either a double or single.

Conversions between the various formats require several tricks. Converting from a string of binary characters to a logical vector involves the use of a comparison statement. Surprisingly, the logical data type requires one byte per element, which is strange because only one bit should be sufficient for a boolean value. Thus, using a logical vector will not save memory. An explicit type cast is not even necessary.

Converting back to a binary string from a logical or numerical vector requires an addition of 48 and a cast to the character data type. Note that logical data are implicitly cast to the data type of the other operand in an expression.

Conversions between numerical and logical vectors are more simple, as they only require casts to those classes, as shown in the examples above. The functions described in this post and the last post have been submitted to the Matlab Central File Exchange:.

Please feel free to download this package and use it. If you have any comments or suggestions, please leave them on the File Exchange website. Hopefully, the techniques discussed in this post will be useful for you. In the next post, the pitfalls of using floating point numbers in comparison statements and the solutions to these pitfalls will be discussed.

Your email address will not be published. It was good, can you please provide us some examples also on Simulink Modeling. Leave a Reply Cancel reply Your email address will not be published.

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