TTL voltage profile and noise margin; Gray code

Input–output voltage profile of TTL

The profile shows the voltage ranges for logic 0 and 1 at the output of a driving gate and at the input of a receiving gate ($V_{CC} = 5$ V):

  Output (driving)       Input (receiving)
 5.0 +--------+         5.0 +--------+
     | HIGH   |             | HIGH   |
 2.4 +--------+ VOH(min) 2.0 +--------+ VIH(min)
     |invalid |  NM_H=0.4   | indet. |
 0.4 +--------+ VOL(max) 0.8 +--------+ VIL(max)
     | LOW    |  NM_L=0.4   | LOW    |
 0.0 +--------+         0.0 +--------+

Inputs between 0.8 V and 2.0 V are not allowed (indeterminate).

Noise margin

Noise margin is the largest noise voltage that can be added to a valid output without the next input reading a wrong level:

$$\begin{aligned} NM_H &= V_{OH(min)} - V_{IH(min)} = 2.4 - 2.0 = 0.4\ \text{V} \\ NM_L &= V_{IL(max)} - V_{OL(max)} = 0.8 - 0.4 = 0.4\ \text{V} \end{aligned}$$

So standard TTL has a noise margin of 0.4 V in both states.

Gray code

Gray code is an unweighted, unit-distance (reflected binary) code: successive numbers differ in only one bit. This avoids false intermediate codes when several bits change together, so it is used in shaft encoders, K-map ordering and error reduction. Binary to Gray: $G_{n} = B_{n}$ (MSB), $G_i = B_{i+1} \oplus B_i$.