Comparators

The basic function of a comparator is to compare the magnitudes of two binary quantities to determine the relationship of those quantities. In its simplest form, a comparator circuit determines whether two numbers are equal.

Equality

 the exclusive-NOR gate can be used as a basic comparator because its output is a 0 if the two input bits are not equal and a 1 if the input bits are equal. Figure shows the exclusive-NOR gate as a 2-bit comparator.

FIGURE 1 Basic comparator operation.

In order to compare binary numbers containing two bits each, an additional exclusive-NOR gate is necessary. The two least significant bits (LSBs) of the two numbers are compared by gate G1, and the two most significant bits (MSBs) are compared by gate G2, as shown in Figure 2. If the two numbers are equal, their corresponding bits are the same, and the output of each exclusive-NOR gate is a 1. If the corresponding sets of bits are not equal, a 0 occurs on that exclusive-NOR gate output.

FIGURE 2: Logic diagram for equality comparison of two 2-bit numbers.

In order to produce a single output indicating an equality or inequality of two numbers, an AND gate can be combined with XNOR gates, as shown in Figure 3. The output of each exclusive-NOR gate is applied to the AND gate input. When the two input bits for each exclusive-NOR are equal, the corresponding bits of the numbers are equal, producing a 1 on both inputs to the AND gate and thus a 1 on the output. When the two numbers are not equal, one or both sets of corresponding bits are unequal, and a 0 appears on at least one input to the AND gate to produce a 0 on its output. Thus, the output of the AND gate indicates equality (1) or inequality (0) of the two numbers. Example illustrates this operation for two specific cases.

EXAMPLE : 

Apply each of the following sets of binary numbers to the comparator inputs, and determine the output by following the logic levels through the circuit.

(a) 10 and 10 

(b) 11 and 10


Solution : 

(a) The output is 1 for inputs 10 and 10,


(b) The output is 0 for inputs 11 and 10, 


the basic comparator can be expanded to any number of bits. The AND gate sets the condition that all corresponding bits of the two numbers must be equal if the two numbers themselves are equal.

Inequality

In addition to the equality output, fixed-function comparators can provide additional outputs that indicate which of the two binary numbers being compared is the larger. That is, there is an output that indicates when number A is greater than number B (A > B) and an output that indicates when number A is less than number B (A < B), as shown in the logic symbol for a 4-bit comparator in Figure 3 

FIGURE 2: Logic symbol for a 4-bit comparator with inequality indication

To determine an inequality of binary numbers A and B, you first examine the highest-order bit in each number. The following conditions are possible:

1. If A3 = 1 and B3 = 0, number A is greater than number B.

2. If A3 = 0 and B3 = 1, number A is less than number B.

3. If A3 = B3, then you must examine the next lower bit position for an inequality.

These three operations are valid for each bit position in the numbers. The general procedure used in a comparator is to check for an inequality in a bit position, starting with the highest-order bits (MSBs). When such an inequality is found, the relationship of the two numbers is established, and any other inequalities in lower-order bit positions must be ignored because it is possible for an opposite indication to occur; the highest-order indication must take precedence.

IMPLEMENTATION: 4-BIT MAGNITUDE COMPARATOR

Fixed-Function Device The 74HC85/74LS85 pin diagram and logic symbol are shown in Figure 4. Notice that this device has all the inputs and outputs of the generalized comparator previously discussed and, in addition, has three cascading inputs: A < B, A = B, A > B. These inputs allow several comparators to be cascaded for comparison of any number of bits greater than four. To expand the comparator, the A < B, A = B, and A > B outputs of the lower-order comparator are connected to the corresponding cascading inputs of the next higher-order comparator. The lowest-order comparator must have a HIGH on the A = B input and LOWs on the A < B and A > B inputs.


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