Digital comparators

Comparators check two numbers, A and B, against one another, the rela­tions of interest being A = B, A > B and A < B. We shall first consider com­parators which determine whether two binary numbers are equal (identity comparators). The criterion for this is that all corresponding bits of the two numbers are identical. The comparator will produce at its output a logic 1 if the numbers are equal, otherwise a logic 0. In the simplest case, the two numbers consist of only one bit each; to compare them, the equiv operation (exclusive-nor gate) may be used. Two AT-bit numbers are compared bit by bit using an equiv circuit for each binary digit and the outputs are combined by an and gate, as shown in Fig. 1.68.

Fig. 1.68 - Identity comparator for two N-bit numbers.

IC-types:

2x8 inputs: SN74LS688 (TTL) from Texas-Instr.

2x9 inputs: Am29809 (TTL) from AMD.

2 x 10 inputs: SN74LS460 from MMI.

Comparators have a wider range of application if, in addition to indicating equality, they can also determine which of two numbers is the larger. Such circuits are known as magnitude comparators. To enable a comparison of the magnitude of two numbers, their code must be known, and for the following, we assume that both numbers are straight binary coded, i.e. that

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The simplest case is again that of comparing two single-bit numbers. The formulation of the logic functions is based on the truth table of Fig. 1.69. From these, we can directly obtain the circuit in Fig. 1.70. The following algorithm is used for comparing numbers consisting of more than one bit: To begin with, the most significant bit (MSB) of A is compared with the MSB of B. If they are different, these bits are sufficient to determine the result. If they are equal, the next lower significant bit must compared, etc. If the identity variable of digit is denoted by g, as in Fig. 1.68, the magnitude comparison of an W-digit number is given by the general relation

Fig. 1.69 - Truth table of a 1-bit magnitude Fig. 1.70 - 1-bit magnitude

comparator. comparator.

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1C types:

for 5-digit comparison: MC 10166 (ECL)

for 8-digit comparison: SN 74 LS682 . . . 689 (TTL).

The circuits can be cascaded serially or in parallel, Fig. 1.71 showing the serial method. When the 3 most significant bits are the same, the outputs of comparator C₁ determine the result, as they are connected to the LSB inputs of comparator C₂ (LSB = least significant bit).

When comparing many-bit numbers it is better to employ parallel cascading, as in Fig. 1.72, since the propagation delay time is shorter.

F ig. 1.71 - Serial magnitude comparator.

Fig. 1.72 - Parallel magnitude comparator.

2 Sequentional Circuits

2.1 Circuritry of flips

Transistor T₁ is on when a positive voltage is dropped across resistor R₁ or resistor R₂. If we also take into account the level inversion produced by the transistor, we can see that components R_{1 ,} R ₂, T₁ 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 - Flip-flop comprising nor gates. Fig. 2.2 - Truth table.