bits
- Thread starter Olson
- Start date
AlChuck
Well-known member
BInary digiT
The binary number system has two digits, 0 and 1. Computers are devices based on the fact that it's easy to have two easily distinguished electrical states, on and off, which corresponds to the 0 and 1 in binary.
Now a single bit can only represent two possible values, 0 or 1. To represent more distinct values, you need numbers made of multiple digits. This works just like the usual everyday base ten number system with ten digits, 0-9. In base 10, one digit can be one of ten distinct values; a two-digit number (00-99) can be one of 100 distinct values, or ten (the number of digits) squared. A three digit number (000-999) can be one of 1000 distinct values, or ten cubed (10 to the third power). And so on. The rule for all number systems is that each extra digit gives you the number of digits in the system times more numbers.
So in base 2, a 2-digit number can represent 2 squared, that is, 2x2 or 4 distinct values (00, 01, 10, and 11); a 3-digit number can represent 2 cubed, that is, 2x2x2 or 8 distinct values (000, 001, 010, 011, 100, 101, 110, 111); a 4-digit number 2 to the fourth power, that is, 2x2x2x2 or 16 distinct values... and so on.
Therefore, a 16-bit binary number can have 2-to-the-16th-power or 65,536 distinct values, while a 24-bit binary number can have 16,777,216 distinct values...
Geesh, I can't believe I'm doing this... I hope this helps.. if it makes no sense, get a basic book on computers and it should have a clearer explanation.
-AlChuck
The binary number system has two digits, 0 and 1. Computers are devices based on the fact that it's easy to have two easily distinguished electrical states, on and off, which corresponds to the 0 and 1 in binary.
Now a single bit can only represent two possible values, 0 or 1. To represent more distinct values, you need numbers made of multiple digits. This works just like the usual everyday base ten number system with ten digits, 0-9. In base 10, one digit can be one of ten distinct values; a two-digit number (00-99) can be one of 100 distinct values, or ten (the number of digits) squared. A three digit number (000-999) can be one of 1000 distinct values, or ten cubed (10 to the third power). And so on. The rule for all number systems is that each extra digit gives you the number of digits in the system times more numbers.
So in base 2, a 2-digit number can represent 2 squared, that is, 2x2 or 4 distinct values (00, 01, 10, and 11); a 3-digit number can represent 2 cubed, that is, 2x2x2 or 8 distinct values (000, 001, 010, 011, 100, 101, 110, 111); a 4-digit number 2 to the fourth power, that is, 2x2x2x2 or 16 distinct values... and so on.
Therefore, a 16-bit binary number can have 2-to-the-16th-power or 65,536 distinct values, while a 24-bit binary number can have 16,777,216 distinct values...
Geesh, I can't believe I'm doing this... I hope this helps.. if it makes no sense, get a basic book on computers and it should have a clearer explanation.
-AlChuck
drstawl
Banned
AlChuck made a valiant start here. As related to digital audio, the bits are storing individual samples, which are instantaneous representations of the amplitude of an audio signal. The more possible states (more bits) available, the closer the approximation to the original analog signal it can theoretically be.
BUT- when you get past 16 bits, which is CD quality as to sample size, the more the quality (accuracy) of the circuitry that converts the analog signal into digital and back again will come into play.
And you also have to consider sample FREQUENCY, which means how far apart in time the individual samples are taken.
44.1 KHz samples are taken ~22.7 microseconds apart.
96 KHz samples are taken ~10.4 microseconds apart.
BUT- when you get past 16 bits, which is CD quality as to sample size, the more the quality (accuracy) of the circuitry that converts the analog signal into digital and back again will come into play.
And you also have to consider sample FREQUENCY, which means how far apart in time the individual samples are taken.
44.1 KHz samples are taken ~22.7 microseconds apart.
96 KHz samples are taken ~10.4 microseconds apart.
camn
Active member
a 16 bit sample = 0.001010101101101 , essentially.
a 24 bit sample = 0.011010010100101001101111 , essentially
Now the REASON to use 24-bit is mathematic. Imagine you were adding and mulitpying these kinds of numbers a LOT of times (which is what happens when you apply DSP)... everytime you have to round that last digit... so you get less cumulative error with hight bit depth.
thats it, and thats all.
xoxo
a 24 bit sample = 0.011010010100101001101111 , essentially
Now the REASON to use 24-bit is mathematic. Imagine you were adding and mulitpying these kinds of numbers a LOT of times (which is what happens when you apply DSP)... everytime you have to round that last digit... so you get less cumulative error with hight bit depth.
thats it, and thats all.
xoxo
AlChuck
Well-known member
bvaleria,
Actually there's no law that says you can't have binary fractions... but all the binary manipulations in computers are integer ones (addition and subtraction and shifts left and right). So when talking about binary numbers in the context of computing and DSP, etc., yup, no decimal points.
-AlChuck
Actually there's no law that says you can't have binary fractions... but all the binary manipulations in computers are integer ones (addition and subtraction and shifts left and right). So when talking about binary numbers in the context of computing and DSP, etc., yup, no decimal points.
-AlChuck
camn
Active member
you geeks, I was trying to be illustrative! I should shove my advanced mathematics degree up your asses.
xoxo
ps. and when you convert a binary to base 10, it can totally have decimals. But you, of course, never would.
Thanks for helping me out, tho, fellas. I, sniff, knew I could count on you!
xoxo
ps. and when you convert a binary to base 10, it can totally have decimals. But you, of course, never would.
Thanks for helping me out, tho, fellas. I, sniff, knew I could count on you!
) *SHEESH*