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TABLE 4-5. MAXIMAL ERRORS WHEN DIFFERENTNUMBERS OF BITS ARE USED TO APPROXIMATE ANANALOG SIGNALNumber Number of Maximal Quantizationof Bits Values Error (%)1 2 252 4 12.53 8 6.28 256 0.2012 4,096 0.012N-bit signal is restricted to 2 N possible values. The quantization error is similar tothe error introduced when a number is "rounded off." Table 4-5 lists the maximalpercent errors associated with digital signals of different numbers of bits.There are additional sources of error in analog-to-digital conversion other thanthe sampling and quantization effects described above. For example, some averagingof the analog signal occurs at the time of sampling, and there are inaccuracies in thequantization process. In summary, a digital signal can only approximate the value ofan analog signal, causing a loss of information during analog-to-digital conversion.No analog signal is a perfect representation of the quantity being measured.Statistical effects in the measurement process and stray electronic voltages ("noise")cause every analog signal to have some uncertainty associated with it. To convert ananalog signal to digital form without a significant loss of information content, theADC must sample at a sufficiently high rate and provide a sufficient number of bitsso that the error is less than the uncertainty in the analog signal being digitized. Inother words, an analog signal with a large signal-to-noise ratio (SNR) requires anADC providing a large number of bits to avoid reducing the SNR.It is often necessary to convert a digital signal to analog form. For example, to displaydigital images from a CT scanner on a video monitor, the image informationmust be converted from digital form to an analog voltage signal. This conversion isperformed by a digital-to-analog converter (DAC). It is important to recognize thatthe information lost by analog-to-digital conversion is not restored by sending thesignal through a DAC (Fig. 4-3).Analog input t t t t tSignalSamplingFIGURE 4-3. Analog-to-digital (ADC) conversion and digital-to-analog (DAC) conversion. In this figure,a 2-bit ADC samples the input signal five times. Note that the output signal from the DAC is onlyan approximation of the input signal to the ADC becausethe 2-bit digital numbers produced by theADC can only approximate the continuously varying analog signal.