Binary Signals - Maple Programming Help

Home : Support : Online Help : Math Apps : Engineering and Applications : MathApps/BinarySignals

Binary Signals

Background

Digital devices communicate through two symbols which can be conveniently called 1 and 0. Any information can be decomposed into a binary signal, that is a signal consisting of only 1's and 0's arranged in some order. For example, "5" might be written as "101" in binary, and "cat" might be written as "011000110110000101110100". Although this seems very hard to read as humans, machines are only able to read (and write) in binary. It is clear that words can be very long in binary, but they only consist of two symbols so they are ultimately very simple.

We transmit binary signals daily through calling or texting a friend and, of course, typing on a computer. For a digital telephone, the binary signal might be pulses of light (1 = pulse of light, 0 = no pulse), which the receiver converts back to audible signals so that we may carry on a conversation. The transmission methods can include light pulses, voltage levels (e.g. 5V represents 1,  0V represents 0), varying current levels and sound pulses/intensities. The transmission mediums can include various types of cables (such as coaxial or fiber optic), liquids and gases or even empty space (radio, satellite, etc).

Encoding

Encoding refers to how the signal is represented and is a very important factor in how well the receiver interprets the signal. The criteria for signal encoding includes:

 • Data transfer rate: A higher data transfer rate means more efficient communication signal, but can also increase the rate of error.
 • Signal to noise ratio: High signal to noise ratio decreases the rate of error.
 • Ease of clocking: How easy it is to determine the start and end of each bit and thus for the receiver to synchronize with the signal.
 • Bandwidth: Bandwidth is the maximum feasible data transfer rate.

The following activity demonstrates some of the various encoding techniques and provides a little bit of information about each. You can generate up to a 24-bit binary number by sending pulses of high and low voltage. The oscilloscope will show you what a perfect signal looks like in the selected encoding type. Afterwards, you can see the decimal equivalent of the binary number that you have generated.

 Signal Encoding Type:  UnipolarBipolarReturn To ZeroManchesterAlternate Mark Inversion

Advantages of Binary Signals

 • Clear and straightforward: everything above a certain threshold is high and everything below that same threshold is low
 • Easy and simple
 • Patterns can be used to represent anything: letters, numbers, symbols, etc.
 • Can be interpreted correctly despite a lot of noise
 • Even if the signal is not perfectly horizontal, as long as it is above the threshold, then it is considered a 1.

 What's Next This Math App gives a brief introduction to signals and communications between electronic devices. The next question that might come to mind is what operations can be performed on these signals? Also, how can electronic devices, such as computers, perform calculations using these signals? This discussion leads into the topic of logic gates. These logic gates can take multiple signals as their inputs and produce an output signal by performing an operation on the inputs. Furthermore, combinations of these logic gates can be used to perform calculations (such as basic binary addition). Check out the Logic Gates Math App for more information.

 More MathApps