Information in terms of usability (useful/useless), eg. usability of noisy information
A good example is the basic addition (+) operation. A function as simple as addition can be information lossy. Below are some demonstrations
- In Communication systems additions occur in:
i) Dispersion of signal due to convolution
ii) Additive Noise (presence of noise is highly undesirable in communication systems)
- In Computer systems imagine that we want the computer to add (an adder) inputs A and B resulting in output signals S (sum) and C (carry).
(for 3 + 1 getting to four, 0 is in sum place and 1 gets carried to carry place thus resulting in (0,1))
In the above adder, output symbols ⟨S, C⟩ cannot detect symbol source. For instance output symbols (1, 1) could be due to A + B (format) either 2 + 3 or 3 + 2. Therefore it is information lossy.
However this is the way addition occurs and hence unlike communication systems information loss in an adder is useful and it is a controlled loss.
