Help with understanding a conversion problem

[morjo619]

Hello,

I trying to figure out an equation on how to convert bit into Megabytes. I found a sight that has the equation, but my math skills are poor and I'd like to understand step-by-step how they are able to solve the conversion.


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http://www.symantec.com/business/suppor ... =TECH36554

When investigating performance related issues, sometimes the logs report performance in bits per second. This TechNote provides a method for converting bits per second into Megabytes per second, which is a more common measurement.

First, convert the number of bits to bytes by dividing by 8:

1 byte
100,000,000,000,000 bits * --------- = x bytes
8 bits

(Notice that the 'bits' cancel, leaving the unit 'bytes' in the answer.) I'm having a hard time understanding this concept -- can someone please help me break it down??

Then take that answer and convert it to Kilobytes by dividing by 1024:

1 Kilobyte
x bytes * ------------- = y Kilobytes
1024 bytes

(Again, the 'bytes' cancel, leaving the unit 'Kilobytes' in the answer.)

Then take that answer and convert it to Megabytes by dividing by 1024 once again:

1 Megabyte
y Kilobytes = * ---------------- = z Megabytes
1024 Kilobytes

Once you find z, you have your answer. Incidentally, you can continue this beyond Megabytes:
1024 Megabytes = 1 Gigabyte and 1024 Gigabytes = 1 Terabyte.

 

[JeffM]

This is called dimensional analysis.

Here is the basic idea.

8 bits = 1 byte.

We want to get rid of bits and go to bytes.

So divide both sides of the equation by 8 bits.
8 bits / 8 bits = 1 = 1 byte / 8 bits.
So we can multiply 1 byte / 8 bits times any number without changing what that number means because multiplying by 1 does not change anything.
6 * 1 = 6. 4 * 1 = 4. And so on.

1024 bytes = 1 kilobyte.
We want to get rid of bytes. So divide both sides by 1024 bytes.
1024 bytes / 1024 bytes = 1 = 1 kilobyte / 1024 bytes.

1024 kilobytes = 1 megabyte.
We want to get rid of kilobytes. So divide both sides by 1024 kilobytes.
1024 kilobytes / 1024 kilobytes = 1 = 1 megabyte / 1024 kilobytes.

Note that we have three fractions with units attached to numerator and denominator that are equivalent to the dimensionless number 1.
1 * 1 * 1 = 1.
So we can multiply these fractions together without fundamentally changing anything.
(1 byte / 8 bits) * (1 kilobyte / 1024 bytes) * (1 megabyte / 1024 kilobytes) = 1 * 1 * 1 = 1.
But note that byte is in the numerator of the first fraction and the denominator of the second fraction so bytes cancel.
And kilobyte is in the numerator of the second fraction and the denominator of the third fraction so kilobytes cancel.
So the fraction simplifies to [1 megabyte /(8 * 1024 * 1024)] bits = (1 megabyte / 8,388,608 bits) = 1.

Now it is simple to multiply b bits times (1 megabyte / 8,388,608 bits). Again bits cancel, leaving an answer expressed in megabytes.

Technically this is how all conversion formulas work.

Does this help?