Electrical Engineering-Intro to Digital

What are the basic goals for Digital systems? One of the key properties of digital systems is its data storage accuracy and resistance to corruption. A basic example where we can apply this idea is the storage of information in Magnetic tapes. So if we assume some magnetic reader/writer using some inductance principle to store information on some tape, we can see that there must be some noise by necessity due to random thermal effects in the data. Thus we have some signal to noise ratio.

In an analog sense, if we want to get a better S/N ratio, we would make the magnetic tape wider. We can take

W = Β x W₀

With our increase in width, we can increase our Signal in analog by

S = Β x S₀

However our noise will increase by a factor of

N = Β^1/2 x N₀

S/N = Β^1/2

so if we want a S/N of 10³, we would need a Β of 10⁶ over some initial length.

In a digital sense, since we are storing information in on and off bits of information, our signal increases as

S = 2 ^Β

However our Noise will remain as 1 due to the inaccuracy of the least bit.

N = 1

S/N = 2 ^Β / 1

so here we only need a Β = 10, which is a huge decrease in the width necessary for the same increase in accuracy.