# 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 numbers Binary equivalent Decimal numbers 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 us 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

We can express the following two decimal numbers in eight bit binary :

27 ONE HUNDRED AND TWENTY EIGHT 0 SIXTY FOUR 0 THIRTY TWO 0 SIXTEENS 1 EIGHTS 1 FOURS 0 TWOS 1 ONES 1 = 00011011
53 ONE HUNDRED AND TWENTY EIGHT 0 SIXTY FOUR 0 THIRTY TWO 1 SIXTEENS 1 EIGHTS 0 FOURS 1 TWOS 0 ONES 1 = 00110101

### Conversion of analogue to digital - sampling an analogue signal

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

The graph shows an analogue signal - the blue line. The value of this signal is 'sampled' at a number of points, in this case 5 ms apart and the value at each of these points is shown in the table.

 Time (ms) Signal intensity (decimal) Signal intensity (binary) Time (ms) Signal intensity (decimal) Signal intensity (binary) 0 78 01001110 75 56 00111000 5 104 01101000 80 80 01010000 10 65 01000001 85 62 00111100 15 71 01000111 90 130 10000010 20 80 01010000 95 95 01011111 25 35 00100011 100 30 00011110 30 116 01110100 105 62 00111110 35 110 01101110 110 75 00111000 40 46 00101110 115 20 00010100 45 60 00111100 120 120 01111000 50 98 01100010 125 115 01110011 55 72 01001000 130 36 00100100 60 60 00111100 135 83 01010011 65 82 01010010 140 92 01011100 70 82 01010010

The following graph shows only these sampled values with the analogue line removed.

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 or noise.

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© Keith Gibbs 2020