<Dd> S N R = 3 × 2 2 n 1 + 4 P e × (2 2 n − 1) m m (t) 2 m p (t) 2 (\ displaystyle \ mathrm (SNR) = (\ frac (3 \ times 2 ^ (2n)) (1 + 4P_ (e) \ times (2 ^ (2n) - 1))) (\ frac (m_ (m) (t) ^ (2)) (m_ (p) (t) ^ (2)))) </Dd> <Dl> <Dd> P e (\ displaystyle P_ (e)) is the probability of received bit error </Dd> <Dd> m p (t) (\ displaystyle m_ (p) (t)) is the peak message signal level </Dd> <Dd> m m (t) (\ displaystyle m_ (m) (t)) is the mean message signal level </Dd> </Dl> <Dd> P e (\ displaystyle P_ (e)) is the probability of received bit error </Dd> <Dd> m p (t) (\ displaystyle m_ (p) (t)) is the peak message signal level </Dd>

The increase in signal to quantization noise ratio for a uniform pcm by an extra bit is