# What's the relationship between samples and bits?

I was talking to a friend today that I have a transmitter which is capable of sending 128 samples/second. Note that each sample is a voltage level represented by a floating point decimal. He then insisted that I call it a 7 bit system since 128 is 2^7.

What useful information can I possible get from representing the samples/second in number of bits? What can each bit physically represent?

Your transmitter can send 128 samples of data. Each sample contains a x number of bits depending on your transmitter. If your transmitter is a 8 bit transmitter then you can send 128 times a 8 bit sample in one second.

• Could you clarify what you mean by "each sample contains x number of bits"? This is the part of the relationship I'm not sure of. Do you mean that since this transmitter is designed to send x bits, and each sample is an integer, therefore any representation of this integer will not be larger than x bits? i.e. 4 bit system, the largest integer that can be sent is 1111? – Carlos - the Mongoose - Danger Oct 30 '14 at 10:35
• yes, if you have a 4 bit system the largest digital number you can send is 1111. this number can then be send 128 times in one second. – T J Oct 30 '14 at 11:05

Your friend confuses two completely different things.

The number of bits per sample tells how many distinct values you can have: be it 8, 10, 12 or whatever number n of bits means you can have 2^n distinct values. On a CD, you have 16 bit samples, and thus 65536 different values.

The number of samples per second is completely unrelated to that. E. g., on a CD, you have 44100 samples per second.

Your friend is confusing sampling with encoding. Your sampling rate is determined by the frequency content of the signal being sampled. the bit depth, ideally is limited by maximum signal excursion on the high end and by noise on the low end.

With digitization you have distinct code encoded in binary format for each signal level. If you have a discreet set of steps of say 0, 1 ,2, 3 ... they are represented 0 = 000, 1 = 001, 2= 010, 3 = 011 etc. in the digital domain. But the 0,1,2,3 steps can easily be 0, 0.1, 0.2, in some signal quantity, like voltage. This is dictated by the conversion constant of the convertor, which might say 100 mv/DN (millivolt per Digital Number).

If you are fitting an 8 bit sample in say 2 volts of signal you have 256 states in 3.0 V and thus 7.8125 mV/DN.

In fact you can have a sampled system that is still analog. These devices (uncommon now) are called BBD (Bucket Brigade devices) AKA CCD (Charge Coupled Devices) - which found their main use as Imaging devices, but started out as signal sampling and processing devices.

• This is nonsense: Another name for digitization is BDC (Binary Coded Decimal). – pjc50 Oct 30 '14 at 10:12
• @pjc50 What are you talking about? BCD is a simply the fact that in an encoding system there is a correspondance of 0 = 000, 1 = 001, 2= 010, 3 = 011 etc. etc. I'll edit to add more material but you're waaay off base. – placeholder Oct 30 '14 at 10:16
• BCD is about mapping e.g. decimal 21 to 0010 0001 rather than 0001 0101. – pjc50 Oct 30 '14 at 12:00
• Agreed, BCD refers to encodings where only the values 0-9 are used in each 4-bit nibble. – The Photon Oct 30 '14 at 16:43
• @pjc50 Aw crap, that's what I get for being up at 4 AM... You're right about the BCD, I was looking for a word that used to be used for the usual binary encoding, because there are different binary codings, braille being one, and my brain tricked me. – placeholder Oct 31 '14 at 1:03