In this post, we will explore bit depth, an essential concept in acoustics. If you are unfamiliar with analog and digital, please refer to relevant posts. To convert an analog signal to digital, the process involves sampling and quantization.
Link to Analog and Digital document
To convert an analog signal to digital, the process involves sampling and quantization. Sampling refers to the extraction of samples at regular intervals from a continuous analog signal. In this phase, the analog signal is sampled momentarily for digitization, represented as discrete numerical values.
Quantization is the process of mapping the sampled analog values to the nearest discrete values. It approximates the sampled signal to the nearest digital value. At this point, the bit depth determines the number of possible values that the signal can take. Higher bit depth allows for a more nuanced representation of values, leading to more accurate signal reproduction.
Through these processes, analog signals are stored, processed, and transmitted in digital form. They are then converted back to analog signals for playback as sounds we can hear.
It’s important to understand what a bit is at this point. A bit, short for “Binary Digit,” is the smallest unit for representing digital data. A bit can have one of two values, typically represented as 0 or 1.
Bits serve as the basic unit for representing information in computer systems. Using binary code, various types of data such as numbers, characters, images, and sounds can be represented. For example, an 8-bit binary code can express 256 different values through an 8-digit number composed of 0s and 1s.
Bits play a vital role in the basic data processing and communication in computer systems. Combining multiple bits allows for the representation of more complex data, and the number of bits affects the range and precision of the data. The more bits used, the higher the number of value combinations and the greater the precision.
For example, 8-bit can represent 2^8 (256) different values, ranging from numbers 0 to 255, alphabets, and symbols. Similarly, 16-bit can represent 2^16 (65536) values, and 32-bit can represent 2^32 (about 4.3 billion) values.
Bit depth refers to the number of bits used in the quantization process. It determines the number of distinct values along the same axis in a digital signal, reflecting the granularity of the signal. Higher bit depth allows for more intricate levels of signal representation but requires more storage space.
Higher bit depths offer more accurate digital representations of original analog signals, but this means using more bits to represent the data. Therefore, selecting the bit depth becomes an important consideration when storing or transmitting large data like digital audio or images.
Floating Point?
Floating Point representation in bit depth differs from integer types, as it allows for the expression of real numbers, which can have values below the decimal point. Floating-point representation typically follows the IEEE 754 standard, which uses normalized forms and consists of a sign bit, exponent bits, and significand bits.
For example, a 32-bit floating-point in IEEE 754 single-precision consists of 1 sign bit, 8 exponent bits, and 23 significand bits. Each of these bits follows various rules and formats for representing real numbers.
16-bit floating-point:
Digits: 1 bit (Sign) + 5 bits (Exponent) + 10 bits (Significand) = 16 bits
Dynamic Range: approximately ±6.55 × 10^416-bit integer:
Digits: 16 bits
Dynamic Range: approximately -32,768 to 32,76732-bit floating-point:
Digits: 1 bit (Sign) + 8 bits (Exponent) + 23 bits (Significand) = 32 bits
Dynamic Range: approximately ±3.40 × 10^3832-bit integer:
Digits: 32 bits
Dynamic Range: approximately -2,147,483,648 to 2,147,483,64764-bit floating-point:
Digits: 1 bit (Sign) + 11 bits (Exponent) + 52 bits (Significand) = 64 bits
Dynamic Range: approximately ±1.80 × 10^30864-bit integer:
The above explains the typical ways floating-point and integer types are represented based on their bit count. Note that specific systems or programming languages may differ.
Digits: 64 bits
Dynamic Range: approximately -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807
Using floating points allows for a broader range and higher precision in representing real numbers. However, unlike integers, they can have limitations in precision and rounding errors below the decimal point. Unless extremely precise calculations are needed, like in scientific and engineering tasks, these limitations are nearly imperceptible. Therefore, floating-point calculations are much more advantageous in audio and video.
Digital Signal Processor (DSP) chips, used in digital mixing consoles or digital signal processors, specialize in real-time audio signal processing. Such devices often prefer integer operations to floating-point operations to tackle latency issues.