# Quantization: levels or intervals?

Assume a 2-bit midrise quantizer with (voltage,codeword) pairs (-3,0),(-1,1),(1,2),(3,3) where step size delta is clearly 2V. Now, calculating PSQNR using the intervals, we have 20log_10(V_peak/qnoise_peak) so Vmax = 3V or 1.5delta. Of course quantization peak error is delta/2 so I should have 1.5delta/(delta/2)=3 in the log.

Here's the problem: textbooks and almost every tutorial I saw take 2^qbits=2^2=4 inside the log function. I feel like the number of levels(4) gets confused with the number of intervals(3). I'm pretty sure I'm the mistaken one, can you explain me how?

Of course, when you get to practical word sizes, N being say 4 or more, the difference between $$\2^N\$$ and $$\2^N-1\$$ becomes insignificant.