Wordlength - Revision history

Brad Johnson at 01:19, 2 March 2019

2019-03-02T01:19:06Z

Brad Johnson at 01:15, 2 March 2019

2019-03-02T01:15:02Z

Brad Johnson at 22:12, 4 August 2017

2017-08-04T22:12:54Z

Brad Johnson at 22:12, 4 August 2017

2017-08-04T22:12:01Z

Brad Johnson at 20:46, 27 August 2014

2014-08-27T20:46:18Z

Brad Johnson at 20:45, 27 August 2014

2014-08-27T20:45:24Z

Brad Johnson at 18:23, 5 July 2012

2012-07-05T18:23:46Z

Brad Johnson at 22:27, 3 July 2012

2012-07-03T22:27:36Z

Brad Johnson at 23:56, 24 February 2012

2012-02-24T23:56:37Z

Brad Johnson at 23:55, 24 February 2012

2012-02-24T23:55:30Z

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 In binary computer technology, information is contained in a digital "word" which is simply a pre-defined collection of a number of individual "[[bits]]." A single bit can only define two "states" as represented by a "1" or a "0." Although useful in limited situations where all-or-nothing yes-or-no information is required; for broader applications more "states" or increments are necessary. By associating a number of bits in a pre-defined manner; a digital word can be used to represent a useful amount of information.
-Similar to the "base ten" system used commonly for day-to-day arithmetic, the “columns” on the left in a binary have a higher value (“more significant”) and the columns on the right have a lower value (“less significant”). For example; in a binary word, the left-most bit is referred to as the “most significant bit” or “msb” and the right-most bit is referred to as the “least significant bit or “lsb.” This is because a “zero” in the lsb column only represents a value of zero and a “one” can only represent a value of one. By contrast, a “zero” in the msb column of a 16 bit word represents a value of zero and a “one” represents a value of 32,786 (or one-half of 2 raised to the sixteenth power). One exception is in the encoding of digital audio using the “two’s compliment” format; in this system the msb is used as the “sign bit” to represent whether the numerical value represented by the other bits in the word refer to a positive or negative portion of the waveform. There are numerous advantages to using two’s compliment encoding for digital audio coding; which are beyond the scope of this discussion.
+Similar to the "base ten" system used commonly for day-to-day arithmetic, the “columns” on the left in a binary have a higher value (“more significant”) and the columns on the right have a lower value (“less significant”). For example; in a binary word, the left-most bit is referred to as the “most significant bit” or “msb” and the right-most bit is referred to as the “least significant bit" or “lsb.” This is because a “zero” in the lsb column only represents a value of zero and a “one” can only represent a value of one. By contrast, a “zero” in the msb column of a 16 bit word represents a value of zero and a “one” represents a value of 32,786 (or one-half of 2 raised to the sixteenth power). One exception is in the encoding of digital audio using the “two’s compliment” format; in this system the msb is used as the “sign bit” to represent whether the numerical value represented by the other bits in the word refer to a positive or negative portion of the waveform. There are numerous advantages to using two’s compliment encoding for digital audio coding; which are beyond the scope of this discussion.
 Early binary computers used 8-bit words to represent up to 256 increments; which made them useful for basic calculations and industrial control; but not for audio. The term “byte” was coined to describe a data word, and although the term byte commonly referred to an 8-bit word, it ''could'' also refer to words with a different number of bits. As technology advanced; 16-bit computers became the norm, and high fidelity digital audio became a possibility. At this time converter technology limited the early 16 bit digital audio systems' quality to much less than its true potential.

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 ==History==
-In binary computer technology, information is contained in a digital "[[word]]" which is simply a pre-defined collection of a number of individual "[[bits]]." A single bit can only define two "states" as represented by a "1" or a "0." Although useful in limited situations where all-or-nothing yes-or-no information is required; for broader applications more "states" or increments are necessary. By associating a number of bits in a pre-defined manner; a digital word can be used to represent a useful amount of information.
+In binary computer technology, information is contained in a digital "word" which is simply a pre-defined collection of a number of individual "[[bits]]." A single bit can only define two "states" as represented by a "1" or a "0." Although useful in limited situations where all-or-nothing yes-or-no information is required; for broader applications more "states" or increments are necessary. By associating a number of bits in a pre-defined manner; a digital word can be used to represent a useful amount of information.
 Similar to the "base ten" system used commonly for day-to-day arithmetic, the “columns” on the left in a binary have a higher value (“more significant”) and the columns on the right have a lower value (“less significant”). For example; in a binary word, the left-most bit is referred to as the “most significant bit” or “msb” and the right-most bit is referred to as the “least significant bit or “lsb.” This is because a “zero” in the lsb column only represents a value of zero and a “one” can only represent a value of one. By contrast, a “zero” in the msb column of a 16 bit word represents a value of zero and a “one” represents a value of 32,786 (or one-half of 2 raised to the sixteenth power). One exception is in the encoding of digital audio using the “two’s compliment” format; in this system the msb is used as the “sign bit” to represent whether the numerical value represented by the other bits in the word refer to a positive or negative portion of the waveform. There are numerous advantages to using two’s compliment encoding for digital audio coding; which are beyond the scope of this discussion.

@@ Line 7: / Line 7: @@
 Similar to the "base ten" system used commonly for day-to-day arithmetic, the “columns” on the left in a binary have a higher value (“more significant”) and the columns on the right have a lower value (“less significant”). For example; in a binary word, the left-most bit is referred to as the “most significant bit” or “msb” and the right-most bit is referred to as the “least significant bit or “lsb.” This is because a “zero” in the lsb column only represents a value of zero and a “one” can only represent a value of one. By contrast, a “zero” in the msb column of a 16 bit word represents a value of zero and a “one” represents a value of 32,786 (or one-half of 2 raised to the sixteenth power). One exception is in the encoding of digital audio using the “two’s compliment” format; in this system the msb is used as the “sign bit” to represent whether the numerical value represented by the other bits in the word refer to a positive or negative portion of the waveform. There are numerous advantages to using two’s compliment encoding for digital audio coding; which are beyond the scope of this discussion.
-Early binary computers used 8-bit words to represent up to 256 increments; which made them useful for basic calculations and industrial control; but not for audio. The term “byte” was coined to describe a data word, and although the term byte commonly referred to an 8-bit word, it ‘’could’’ also refer to words with a different number of bits. As technology advanced; 16-bit computers became the norm, and high fidelity digital audio became a possibility. At this time converter technology limited the early 16 bit digital audio systems' quality to much less than its true potential.
+Early binary computers used 8-bit words to represent up to 256 increments; which made them useful for basic calculations and industrial control; but not for audio. The term “byte” was coined to describe a data word, and although the term byte commonly referred to an 8-bit word, it ''could'' also refer to words with a different number of bits. As technology advanced; 16-bit computers became the norm, and high fidelity digital audio became a possibility. At this time converter technology limited the early 16 bit digital audio systems' quality to much less than its true potential.
 Computer technology continued to advance; and 32 bit computers became available. Due in part to the evolution of computer technology; it was not unusual for 32 bit computers to move information between the CPU and hard drive in pairs of 16 bit words. Practically speaking; digital audio converters with an accuracy of 24 bits are capable of encoding analog audio to the level of accuracy obtainable with very high quality analog circuitry; so even though 24 bit wordlength is not typical of computer technology; it has become a standard in digital audio. In most cases; computer software simply uses two 16 bit words (or a "32 bit word") to represent a 24 bit digital audio word and thus simplify operations. The first 16 bit word contains the most-significant digital audio bits, and the 16 bit word containing the 8 least-significant audio bits simply contains "zeros" in the other (unused) 8 bits.

@@ Line 7: / Line 7: @@
 Similar to the "base ten" system used commonly for day-to-day arithmetic, the “columns” on the left in a binary have a higher value (“more significant”) and the columns on the right have a lower value (“less significant”). For example; in a binary word, the left-most bit is referred to as the “most significant bit” or “msb” and the right-most bit is referred to as the “least significant bit or “lsb.” This is because a “zero” in the lsb column only represents a value of zero and a “one” can only represent a value of one. By contrast, a “zero” in the msb column of a 16 bit word represents a value of zero and a “one” represents a value of 32,786 (or one-half of 2 raised to the sixteenth power). One exception is in the encoding of digital audio using the “two’s compliment” format; in this system the msb is used as the “sign bit” to represent whether the numerical value represented by the other bits in the word refer to a positive or negative portion of the waveform. There are numerous advantages to using two’s compliment encoding for digital audio coding; which are beyond the scope of this discussion.
-Early binary computer used 8-bit words to represent up to 256 increments; which made them useful for basic calculations and industrial control; but not for audio. The term “byte” was coined to describe a data word, and although the term byte commonly referred to an 8-bit word, it ‘’could’’ also refer to words with a different number of bits. As technology advanced; 16-bit computers became the norm, and high fidelity digital audio became a possibility. At this time converter technology limited the early 16 bit digital audio systems' quality to much less than its true potential.
+Early binary computers used 8-bit words to represent up to 256 increments; which made them useful for basic calculations and industrial control; but not for audio. The term “byte” was coined to describe a data word, and although the term byte commonly referred to an 8-bit word, it ‘’could’’ also refer to words with a different number of bits. As technology advanced; 16-bit computers became the norm, and high fidelity digital audio became a possibility. At this time converter technology limited the early 16 bit digital audio systems' quality to much less than its true potential.
 Computer technology continued to advance; and 32 bit computers became available. Due in part to the evolution of computer technology; it was not unusual for 32 bit computers to move information between the CPU and hard drive in pairs of 16 bit words. Practically speaking; digital audio converters with an accuracy of 24 bits are capable of encoding analog audio to the level of accuracy obtainable with very high quality analog circuitry; so even though 24 bit wordlength is not typical of computer technology; it has become a standard in digital audio. In most cases; computer software simply uses two 16 bit words (or a "32 bit word") to represent a 24 bit digital audio word and thus simplify operations. The first 16 bit word contains the most-significant digital audio bits, and the 16 bit word containing the 8 least-significant audio bits simply contains "zeros" in the other (unused) 8 bits.

@@ Line 5: / Line 5: @@
 In binary computer technology, information is contained in a digital "[[word]]" which is simply a pre-defined collection of a number of individual "[[bits]]." A single bit can only define two "states" as represented by a "1" or a "0." Although useful in limited situations where all-or-nothing yes-or-no information is required; for broader applications more "states" or increments are necessary. By associating a number of bits in a pre-defined manner; a digital word can be used to represent a useful amount of information.
-Similar to the "base ten" system used commonly for day-to-day arithmetic, the “columns” on the left in a binary have a higher value (“more significant”) and the columns on the right have a lower value (“less significant”). For example; in a binary word, the left-most bit is referred to as the “most significant bit” or “[[msb]]” and the right-most bit is referred to as the “least significant bit or “[[lsb]].” This is because a “zero” in the lsb column only represents a value of zero and a “one” can only represent a value of one. By contrast, a “zero” in the msb column of a 16 bit word represents a value of zero and a “one” represents a value of 32,786 (or one-half of 2 raised to the sixteenth power). One exception is in the encoding of digital audio using the “two’s compliment” format; in this system the msb is used as the “sign bit” to represent whether the numerical value represented by the other bits in the word refer to a positive or negative portion of the waveform. There are numerous advantages to using two’s compliment encoding for digital audio coding; which are beyond the scope of this discussion.
+Similar to the "base ten" system used commonly for day-to-day arithmetic, the “columns” on the left in a binary have a higher value (“more significant”) and the columns on the right have a lower value (“less significant”). For example; in a binary word, the left-most bit is referred to as the “most significant bit” or “msb” and the right-most bit is referred to as the “least significant bit or “lsb.” This is because a “zero” in the lsb column only represents a value of zero and a “one” can only represent a value of one. By contrast, a “zero” in the msb column of a 16 bit word represents a value of zero and a “one” represents a value of 32,786 (or one-half of 2 raised to the sixteenth power). One exception is in the encoding of digital audio using the “two’s compliment” format; in this system the msb is used as the “sign bit” to represent whether the numerical value represented by the other bits in the word refer to a positive or negative portion of the waveform. There are numerous advantages to using two’s compliment encoding for digital audio coding; which are beyond the scope of this discussion.
 Early binary computer used 8-bit words to represent up to 256 increments; which made them useful for basic calculations and industrial control; but not for audio. The term “byte” was coined to describe a data word, and although the term byte commonly referred to an 8-bit word, it ‘’could’’ also refer to words with a different number of bits. As technology advanced; 16-bit computers became the norm, and high fidelity digital audio became a possibility. At this time converter technology limited the early 16 bit digital audio systems' quality to much less than its true potential.

@@ Line 4: / Line 4: @@
 ==History==
 In binary computer technology, information is contained in a digital "[[word]]" which is simply a pre-defined collection of a number of individual "[[bits]]." A single bit can only define two "states" as represented by a "1" or a "0." Although useful in limited situations where all-or-nothing yes-or-no information is required; for broader applications more "states" or increments are necessary. By associating a number of bits in a pre-defined manner; a digital word can be used to represent a useful amount of information.
 Early binary computer used 8-bit words to represent up to 256 increments; which made them useful for basic calculations and industrial control; but not for audio. As technology advanced; 16-bit computers became the norm, and digital audio became a possibility. At this time converter technology limited the early 16 bit digital audio systems' quality to much less than the potential.
@@ Line 10: / Line 12: @@
 Although excellent quality audio can be encoded to 24 bit digital audio; virtually any time a process is applied to the original 24 bit signal, more than 24 bits will be needed to accurately represent the processed signal. For this reason; most processing is performed with 32 bit or 64 bit precision, and to retain quality the output is only reduced to 24 bit wordlength after [[dither]] and [[noise shaping]] has been applied.
 [[Category:Terminology]]
 [[Category:Audio conversion]]