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==Properties== An advantage of digital circuits when compared to analog circuits is that signals represented digitally can be transmitted without degradation caused by [[noise]].<ref>[[Paul Horowitz]] and Winfield Hill, ''The Art of Electronics 2nd Ed.'' Cambridge University Press, Cambridge, 1989 {{ISBN|0-521-37095-7}} page 471</ref> For example, a continuous audio signal transmitted as a sequence of 1s and 0s, can be reconstructed without error, provided the noise picked up in transmission is not enough to prevent identification of the 1s and 0s. In a digital system, a more precise representation of a signal can be obtained by using more binary digits to represent it. While this requires more digital circuits to process the signals, each digit is handled by the same kind of hardware, resulting in an easily [[scalable]] system. In an analog system, additional resolution requires fundamental improvements in the linearity and noise characteristics of each step of the [[signal chain]]. With computer-controlled digital systems, new functions can be added through software revision and no hardware changes are needed. Often this can be done outside of the factory by updating the product's software. This way, the product's design errors can be corrected even after the product is in a customer's hands. Information storage can be easier in digital systems than in analog ones. The noise immunity of digital systems permits data to be stored and retrieved without degradation. In an analog system, noise from aging and wear degrade the information stored. In a digital system, as long as the total noise is below a certain level, the information can be recovered perfectly. Even when more significant noise is present, the use of [[Redundancy (information theory)|redundancy]] permits the recovery of the original data provided too many errors do not occur. In some cases, digital circuits use more energy than analog circuits to accomplish the same tasks, thus producing more heat which increases the complexity of the circuits such as the inclusion of heat sinks. In portable or battery-powered systems this can limit the use of digital systems. For example, battery-powered [[cellular phone]]s often use a low-power analog front-end to [[amplifier|amplify]] and [[Tuner (radio)|tune]] the radio signals from the base station. However, a base station has grid power and can use power-hungry, but very flexible [[software radio]]s. Such base stations can easily be reprogrammed to process the signals used in new cellular standards. Many useful digital systems must translate from continuous analog signals to discrete digital signals. This causes [[quantization error]]s. Quantization error can be reduced if the system stores enough digital data to represent the signal to the desired degree of [[fidelity]]. The [[Nyquist–Shannon sampling theorem]] provides an important guideline as to how much digital data is needed to accurately portray a given analog signal. If a single piece of digital data is lost or misinterpreted, in some systems only a small error may result, while in other systems the meaning of large blocks of related data can completely change. For example, a single-bit error in audio data stored directly as [[linear pulse-code modulation]] causes, at worst, a single audible click. But when using [[audio compression (data)|audio compression]] to save storage space and transmission time, a single bit error may cause a much larger disruption. Because of the [[cliff effect]], it can be difficult for users to tell if a particular system is right on the edge of failure, or if it can tolerate much more noise before failing. Digital fragility can be reduced by designing a digital system for [[robustness (computer science)|robustness]]. For example, a [[parity bit]] or other error management method can be inserted into the signal path. These schemes help the system detect errors, and then either [[error detection and correction|correct the error]]s, or request retransmission of the data. {{Further|Digital signal conditioning|Signal conditioning}}
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