Page 328 - Physics Coursebook 2015 (A level)

Cambridge International A Level Physics
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Large numbers require more bits. Table 20.2 shows numbers containing 4 bits, although 0011 is the correct way of writing a 4-bit number, rather than writing 11. A digital telephone system commonly transmits numbers containing 8 bits and there are 28 = 256 different 8-bit binary numbers.
Changing an analogue signal into a digital signal involves sampling. In analogue-to digital conversion (ADC), sampling is the measurement of the analogue signal at regular time intervals.
The value of the sampled signal is used to produce a binary number. Each time that the signal is sampled the ADC produces a binary number of a certain number of bits. Since the sample is taken many times per second, many binary numbers are created, one after the other, and this series of 0s and 1s becomes the digital signal that is transmitted.
The process is illustrated in Figure 20.10 where 4-bit binary numbers are produced.
Figure 20.11 shows the result of this conversion back into analogue form. The blue circles show the values of
the voltage, which are each a decimal number formed from a 4-bit binary number. The black line drawn through the circles is the output signal. Some electronic systems contain extra filter circuits that are able to smooth the output, and they produce the blue line as the final output.
The black line, the output, is clearly not exactly the same as the original signal. There are two reasons for this.
1010
1001
1000
0111 0011
When the time t = 0, the numerical value of the voltage signal is 9 as a decimal number. When converted into binary, this number is 1001. When t = 100 μs, the voltage is 10 as a decimal number and 1010 as a binary number.
You will notice that at some values of t the signal is not a whole number on the voltage axis. The nearest number is chosen.
When the output is sampled every 100 μs, a set of binary numbers is produced: (1001), then (1010), then (1001), then (1000), then (1000) and so on. These sets of 4-bit numbers are transmitted one after the other. If they are transmitted a long distance, a regeneration amplifier is used along the way to keep the same pattern of pulses. A digital-to-analogue converter changes the digital signal back into analogue form at the end of the transmission.
10 9 8
6 3 0
10 9 8
6 3
0 0 200
Figure 20.10 Analogue-to-digital conversion.
0 200 400 600 800 1000 Time / μs
1010
1001
1000
0111 0011
Firstly, the sampled signal is not always a whole number. For example, in Figure 20.10 when t = 300 μs the actual voltage is 8.3 V but only the number 8 can be sent, not 8.3.
To improve the sampling, the voltage that corresponds to the difference between 0 and 1 must be decreased. In the above example, the difference between 0 and 1 in binary is 1V and so the signal is ‘accurate’ to only 1V. If the difference between 0 and 1 is made to be 0.1 V then ‘accuracy’ is improved. Adding an extra bit is similar
to having an extra significant figure when measuring a voltage as 8.3 V rather than 8 V. Integers up to 10 need a 4-bit binary number. If the system handles numbers to within 0.1 then 10.0 requires an 8-bit number, which has 128 different possible levels.
The other problem is that the sampling rate is not high enough. The sampling rate is the number of samples made per second. In the example in Figure 20.10, the sample is taken every 100 μs and so the sampling rate is
to another value and back 1 = 10 000 times a second. 0.0001
If the signal changes to another value and back between one sample and the next then no record is made of that change. Obviously the higher the sampling rate, the closer the final signal will be to the original signal.
Figure 20.11 Digital-to-analogue conversion.
400 600 Time / μs
800 1000
Voltage / V
Voltage / V