Digital Signal

Not long ago, most homes in Nepal watched television through an antenna: a metal frame tied to a tall bamboo pole on the roof. Later, cable TV became very popular. In cable TV, a cable company sends programmes to each house through a wire. Today many homes use Dish TV and Internet TV instead. Of these three kinds, the television connected to an antenna gives the poorest sound and picture.

The reason lies in the waves. A transmitter sends out waves, and as they travel through the air they lose energy to the surroundings. By the time they reach a home far away they have become weak, so they produce only a small potential difference (p.d.) across the antenna. The electric current produced in the wire joined to the antenna is weak as well. This current is the modulated signal of the television broadcast: the signal that carries the programme's sound and picture.

Circuits inside the television convert this signal into a digital signal, and the sound and picture are then handled as digital signals. A small electronic part called a transistor does this job. A transistor works like a switch that turns on and off extremely fast, so it can turn a changing current into a string of high and low values.

Cable TV also carries modulated signals in its wire. To watch cable TV on a computer, a cable modem must be connected between the cable and the computer. Dish TV works differently. The dish receives digital signals straight from a satellite and broadcasts those.

Our eyes and ears can only take in light and sound that change smoothly. Signals like these are analogue signals. Digital signals are easy to send and to store, but nobody can see or hear a string of 0s and 1s. So a broadcast needs two conversions. First the analogue signal is changed into a digital signal, which is easy to send and process. Then, at the receiving end, the digital signal is changed back into an analogue signal so that it becomes a picture we can see and a sound we can hear.

Think of recording your voice on a computer and playing it back. The signal changes form in this order:

• You speak, and sound waves reach the microphone.
• The microphone changes the sound into a changing electrical voltage. This is an analogue signal.
• An analogue to digital converter (ADC) changes that voltage into binary data made of 0s and 1s.
• The computer stores and processes the binary data as a digital signal.
• A digital to analogue converter (DAC) changes the binary data back into a changing voltage.
• The speaker turns that voltage into sound waves, and the ear hears your voice again.

Because digital signals are so easy to send, their use has spread widely in information and communication. Mobile phones, the internet and social media all run on them. The active part people now take in social media, and the way their behaviour has changed with it, has given us a new term: digital native, also called digital citizen. Being courteous and behaving positively in online conversations improves a person's online reputation. Online facilities can do a great deal of good, but using them wrongly can badly affect our physical, mental and emotional health.

A physical quantity that changes with time is called a signal. The voltage across a bulb, the temperature of a room, the loudness of a sound: when any of these changes as time passes, it can act as a signal.

A simple circuit shows what a digital signal is. A bulb, a switch and a 5 V source are joined with wires. When the switch is turned on, the potential difference across the two ends of the bulb is 5 V. This is called a high signal and is written as 1. When the switch is turned off, the potential difference across the bulb becomes zero. This is called a low signal and is written as 0.

Now note the state of the switch once every second. Suppose it is off, on, on, off. Written as a signal, this is 0, 1, 1, 0. Drawn on a graph against time, the line jumps straight up from 0 V to 5 V and later drops straight down again. It has flat tops and flat bottoms, and it never stops anywhere in between. This shape is called a square wave.

Inside an electronic device, nobody can press a switch millions of times a second. So devices contain special parts such as transistors, which turn on and off by themselves at great speed and create digital signals.

Now imagine the bulb joined to a regulator knob instead of a switch, so the voltage can be turned up and down slowly. As the knob turns, the voltage rises from 0 V through 3 V to 5 V, then falls back through 3 V to 0 V. The bulb goes from off, to dim, to bright, to dim, and off again. Here the voltage never jumps. It passes through every value in between, so its graph is a smooth curve.

If an alternating current (AC) source is used and the switch is simply left on, the potential difference rises and falls continuously by itself. For a voltage that swings between +5 V and -5 V, the graph is a sine wave. Its highest point is the peak (+5 V) and its lowest point is the valley (-5 V). The sloping part joining a peak to a valley is the slope, where the voltage is changing. The part above the zero line is the positive AC voltage and the part below it is the negative AC voltage. This is an analogue signal.

Much of everyday life is analogue. Our speaking voice, the temperature that rises and falls slowly through the day, and the daylight that changes from morning to evening all change continuously, not in separate steps.

A digital signal uses only two digits, 0 and 1. A number system that uses only these two digits is the binary system, and each 0 or 1 is a binary digit. One binary digit can show only two things. When binary digits are put together, the number of possible patterns grows, and these combinations are what make up digital signals.

Each extra digit doubles the number of combinations, because every earlier pattern can be followed by either 0 or 1. So \( n \) binary digits give \( 2^n \) combinations. Four binary digits give \( 2^4 = 16 \) combinations, from 0000 up to 1111.

Every binary number can be shown with a row of switches. Place four switches side by side. A switch that is on stands for 1 and a switch that is off stands for 0. The number 0110 then means: first switch off, second on, third on, fourth off. Each different pattern of on and off switches stands for different data, and this is exactly how a computer keeps information.

These patterns of 0s and 1s are stored in a computer's memory. The memory capacity of a computer is chosen according to what its user needs. Memory can keep a large amount of data permanently, and users can easily store data in many formats such as text, graphics, audio and video. Memory capacity is measured in units such as bits, bytes, kilobytes (KB), megabytes (MB), gigabytes (GB) and terabytes (TB).

Why 1024 and not 1000? A computer counts in twos, and \( 2^{10} = 1024 \). This is the power of 2 closest to one thousand.

To change a big unit into a smaller one, multiply. To change a small unit into a bigger one, divide. Each step up the table uses 1024, except the step between bytes and bits, which uses 8.

Example 1: How many bits are there in 2 KB?

Step 1: Changing kilobytes into bytes, since 1 KB = 1024 bytes:

\[ 2 \times 1024 = 2048 \text{ bytes} \]

Step 2: Changing bytes into bits, since 1 byte = 8 bits:

\[ 2048 \times 8 = 16384 \text{ bits} \]

So 2 KB holds 16384 bits.

Example 2: A pen drive holds 4 GB. Write this in MB.

Step 1: Multiplying by 1024, since 1 GB = 1024 MB:

\[ 4 \times 1024 = 4096\ \text{MB} \]

Example 3: A song file is 3072 KB. How many MB is it?

Step 1: Dividing by 1024, because MB is the bigger unit:

\[ 3072 \div 1024 = 3\ \text{MB} \]

Check: \( 3 \times 1024 = 3072 \), so the answer is right.

The examples in the last row are worth understanding. The temperature of a room changes slowly and continuously, so it is analogue. The ADC in a digital thermometer's sensor turns it into digits that appear on the screen. A song saved on a computer is digital, stored as 0s and 1s. When it plays, a DAC turns it into a changing voltage, and only then can the speaker produce sound we can hear.