Attenuation: dB = 10 log10(Pr/Ps) loss of power during transmission we transmit 10W and recieve 9W, what's the attenuation in decibels? 10 * log_10 (9W/10W) <- log base 10. or 10 * log (9/10) / log(10) <- any log base (often e). = -0.45757 brush up on logs: https://www.youtube.com/watch?v=sULa9Lc4pck Nyquist Bandwidth C = 2B log2 M Bandwidth is 8kHz, number of votage levels is 4, what's the max capacity? C = 2 * 8000 * log(4)/log(2) <- any log C = 32000.00000 or C = 32kbps if capacitry is 32kbps, and we're using 4 votage levels, what's the bandwidth? .... 8kHz Shannon Capacity --signal to noise ratio in decibels SNRdB = 10 log10 signal power / noise power C = B log2 (1 + SNR) we're transmitting at 31W, noise on the wire estimated to be 1W, bandwidth is 8kHz, what's the max error free capacity? SNR = 31/1 = 31 C = 8000 * log(1 + 31) / log(2) C = 40000 = 40kbps ------ we're transmitting at 40kbps, 2% of the bits arrive flipped. what's the error free capacity of this channel? assume we have a wire that indicates when an error occurs [e.g. 40kbps, a 1 for an error and 0 for no-error]. what's the entropy of this signal? H = -(0.02*log(0.02)/log(2) + (1 - 0.02)*log(1 - 0.02)/log(2) ) H = 0.14144 every symbol (1 or 0) of this "error channel" is actually 0.14144 bits of information. we're transmitting 40kbps of these errors: 40000 * 0.14144. 5657.6bps of errors... total capacity is 40kbps, errors are 5.657kbps, leaving: 40000 - 5657 = 34343 bits/second for error-free-capacity. ~ 34.3kbps max length of LAN: http://theparticle.com/cs/bc/net/ether.pdf MaxLength = (2 × 108) × (51.2 × 10−6/2) = 5120m