Ternary logic ( R =3 ) has three logical states {0, 1, 2}
Quaternary logic ( R = 4) has four logical states {0, 1, 2, 3}
The noise margin is one of the main issues in MVL, if not the main one.
In the case of 0 to Vdd:
The ideal noise margin for ternary logic is: Vdd/4
The ideal noise margin for quaternary logic is: Vdd/6
For more illustration, you can check the ternary and quaternary works and their SNM butterfly curves.
In multi-valued circuits such as ternary and quaternary logic circuits, the noise margin is typically defined as the difference between the input voltage level that would be interpreted as a logical high and the input voltage level that would be interpreted as a logical low, divided by two.
For example, in a ternary logic circuit where the three logic levels are represented by voltage levels V0, V1, and V2, the noise margin would be (V1 - V0)/2 or (V2 - V1)/2, whichever is smaller. Similarly, in a quaternary logic circuit with four logic levels represented by voltage levels V0, V1, V2, and V3, the noise margin would be (V1 - V0)/2, (V2 - V1)/2, or (V3 - V2)/2, whichever is smaller.
The range of the noise margin in multi-valued circuits depends on the specific circuit design and the operating conditions. In general, a larger noise margin provides greater immunity to noise and interference, but may also require higher voltage levels or more complex circuit designs.
As an example, in a ternary logic circuit with voltage levels of 0V, 2.5V, and 5V, the noise margin would be (2.5V - 0V)/2 = 1.25V or (5V - 2.5V)/2 = 1.25V, whichever is smaller. In a quaternary logic circuit with voltage levels of 0V, 1.67V, 3.33V, and 5V, the noise margin would be (1.67V - 0V)/2 = 0.835V, (3.33V - 1.67V)/2 = 0.835V, or (5V - 3.33V)/2 = 0.835V, whichever is smaller.
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