# Analogue and digital signals

An ANALOGUE SIGNAL is one where the waveform in the information follows the original waveform exactly at all times

A DIGITAL SIGNAL is one where the original waveform is sampled at regular intervals and a number given to the value of the disturbance at each of these points.

Binary numbers are used for these sampled values.

Binary is a way of expressing numbers in ones (high voltage value) or zeros (low voltage value) – there is nothing in between. You can have either a 1 or a 0.
In mathematical language you are expressing numbers to the base 2 instead of our normal decimal system where we use the base 10.

 Decimal number Binary equivalent Decimal number Binary equivalent 0 0000 8 1000 1 0001 9 1001 2 0010 10 1010 3 0011 11 1011 4 0100 12 1100 5 0101 13 1101 6 0110 14 1110 7 0111 15 1111

The number of digits in the group gives is the BIT NUMBER. For example all the above numbers are FOUR BIT NUMBERS. Many of your computers are 32 BIT machines – they deal with numbers like:

00110011010011100011000110101011

So we can express the following in numbers in binary :

27: THIRTY TWO 0 SIXTEENS 1 EIGHTS 1 FOURS 0 TWOS 1 ONES 1 = 011011
53: THIRTY TWO 1 SIXTEENS 1 EIGHTS 0 FOURS 1 TWOS 0 ONES 1 = 110101

## Sampling an analogue signal

An example of the conversion from an analogue to a digital signal using sampling is shown below.

The value of the analoque signal is first 'sampled' once every 10 ms.

 Time (ms) Signal intensity (decimal) Signal intensity (binary) 0 78 01001110 5 104 01101000 10 65 01000001 15 71 01000111 20 80 01010000 25 35 00100011 30 116 01110100 35 110 01101110 40 46 00101110 45 60 00111100 50 98 01100010 55 72 01001000 60 60 00111100 65 82 01010010 70 76 01001100 75 56 00111000 80 80 01010000 85 62 00111110 90 130 10000010 95 95 01011111 100 30 00011110 105 62 00000000 110 75 01001011 115 20 00010100 120 120 01110000 125 115 01110011 130 36 00100100 135 83 01010011 140 92 01011100

These sampled analogue readings are then plotted against time.

The following three graphs show the problems with sampling. If you only sample at a few times the resulting curve does not really match the original very well. The red sampled points and the yellow sampled points give different curves from sampling both the red and yellow points and even this does not quite fit the original wave. Therefore the more often you sample the wave the better. In a digital CD the original analogue waveform is sampled a staggering 44 100 times a second and for a DVD it can be double this.

The reason for using binary and not ordinary decimal numbers is to do with interference of the original signal, often called noise.

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