Extracting Sign, Exponent, and Mantissa from 64-bit Machine Number

[Hiche]

Homework Statement

The problem asks us to write a MATLAB function that takes as input a vector 'v' representing a 64-bit machine number in double precision, and extract the sign (t), the exponent (c), and the mantissa (f).

Homework Equations

The Attempt at a Solution

I'm extremely novice at MATLAB and the instructor assigned us a HW and a tutorial without bothering to pass on lectures about the language so bear with me, please.

function [t c f] = GetVector(v)
t = v(1);
c = v(2:12);
f = v(13:64);
end

Now, t will take the values 0 or 1 (the first element of the 64-bit representation), c will take the next 11 bits (the biased exponent), and f takes the remaining 52 bits. Now, my question is, do we have to subtract 1023 from the biased exponent to get e (the exponent) since they asked for the exponent? How exactly do we do that?

I think we have to create another function that converts the binary representation of c into decimal form then subtract 1023 from the 10-based number. If so, will this function do? And how exactly do functions return a value in MATLAB?

function [dec] = Convert2to10(Ibase2)
for i = 1 : length(Ibase2)
    dec = dec + str2num(Ibase2(i)) * 2^(length(Ibase2) - i);
end
end

Thanks in advance.

 

[KataKoniK]

Hello there,

I can help you with your questions and provide some guidance on how to approach this problem. First, let's break down the problem into smaller steps:

1. Understanding the input: The input 'v' is a vector representing a 64-bit machine number in double precision. This means that 'v' contains 64 elements, each representing a single bit in the binary representation of the number. So, for example, if 'v' is [1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0], this represents the binary number 1010101010101010101010101010101010101010101010101010101010101010.

2. Extracting the sign, exponent, and mantissa: The sign bit, represented by 't', is simply the first element of the vector 'v'. The exponent, represented by 'c', is the next 11 bits after the sign bit (bits 2 to 12). The mantissa, represented by 'f', is the remaining 52 bits (bits 13 to 64). So, you are correct in your attempt at the solution.

3. Converting the exponent to decimal form: The exponent in the 64-bit representation is biased, which means that it is not the actual exponent of the number. To get the actual exponent, we need to subtract the bias from the exponent. In this case, the bias is 1023. So, if the exponent is 10001010101 (in binary), the actual exponent would be 10001010101 - 1023 = 1.

4. Converting binary to decimal: Your function to convert binary to decimal looks correct, but it would be better to use MATLAB's built-in