Sequentional Circuits
2.1 Circuritry of flips
Transistor T_{1} is on when a positive voltage is dropped across resistor R_{1} or resistor R_{2}. If we also take into account the level inversion produced by the transistor, we can see that components R_{1 , }R_{ 2}, T_{1} and R_{C} form a nor gate. The same applies to the other half of the circuit. Inserting the appropriate circuit symbols, we obtain the circuit diagram shown in Fig. 2.1 with the associated truth table (Fig. 2.2).
Fig. 2.1  Flipflop comprising nor gates. Fig. 2.2  Truth table.
Sequential logic systems
A sequential logic system is an arrangement of digital circuits which can carry out logic operations and, in addition, store the states of individual variables. It diners from a combinatorial logic system in that the output variables y_{j} are not only dependent on the input variable x_{i}, but also on the previous history which is represented by the state of flipflops.
In the following we shall first discuss the design and operation of integrated flipflops.
Integrated flipflops
We shall now demonstrate the operation of flipflops with reference to gates. This approach defines their basic operation irrespective of the particular technology employed.
Transparent flipflops
By connecting two NOR gates in a feedback arrangement as in Fig. 2.3, we obtain a flipflop which has complementary outputs Q and and two inputs S (Set) and R (Reset).
If the complementary input state S = 1 and R = 0 is applied, we have
and
The two outputs, therefore, assume complementary states. Similarly, for R = 1 and S = 0, the opposite output state is obtained. If we make R = S = 0, the old output state is retained. This explains why RS flipflops are used as memories. When R = S = 1, the two outputs become simultaneously 0; however, the output state is no longer defined when R and S then become simultaneously 0. Consequently, the input state R = S = 1 is generally disallowed. The switching states are summarized in the truth table in Fig. 2.4, with which we are already familiar from the transistor circuit
In Section 9.2 we showed that a logic equation does not change if all the variables are negated and the arithmetic operations (+) and (•) are interchanged. Applying this rule here, we arrive at the RS flipflop comprising NAND gates shown in Fig. 2.5, which has the same truth table as that shown in Fig. 2.4. However, note that the input variables are now and . As we shall be frequently using the RS flipflop comprising NAND gates, we have given its truth table for input variables and in Fig. 2.6.
Fig. 2.3  RS flipflop comprising NOR gates. . Fig. 2.4  Truth table for an RS flipflop.
Fig. 2.5  RS flipflop comprising NAND gates Fig. 2.6 . Truth table for an RS flip flop comprising NAND gates.
Date: 20150112; view: 1085
