1. Unit1: Modeling & Simulation Module5: Logic Simulation Topic: Unknown Logic Value

2. Introduction In any sequential circuit, the output response to any input depends on its initial state. The initial states of memory elements is unpredictable. To process the unknown initial state, simulation algorithms use a separate value, denoted by ‘u’. U  unknown logic value

3. Contd … It is processed along with the binary logic values. Now the Boolean operations will be on 3-valued logic. The value represents one in the logic set {0,1}. Now, ◦ 0  {0} ◦ 1  {1} ◦ U  {0,1}

4. Examples AND (0,U) = AND ({0}, {0,1}) = {AND(0,0), AND(0,1)} = {0,0} = {0} = 0 OR (0,u) = OR ({0}, {0,1}) = {OR(0,0), OR(0,1)} = {0,1} = U NOT (U) = NOT ({0,1} = {NOT(0), NOT(1)} = {1,0} = {0,1} = U

5. Loss of information with 3-valued logic It was shown that NOT(U) = U Similar is the case with the complimentary outputs of a flip-flop whose state is U. The output is actually ‘1’ but is computed to U by the rules of 3-valued logic.

6. Contd … When we have only one state variable, use of complimentary unknown values U, U with these rules U + U = 1, U.U = 0, would solve the problem. Problem with use of U and U with above rules

7. Solution to 3-valued logic problem Use several distinct unknown signals U 1, U 2, …U k One for each state variable Rules U i. U i = 0 U i + U i = 1 But this technique is complex, since some lines would be represented by large Boolean expressions of U i