The Digital Comparator
Another common and very useful combinational logic circuit is that of the Digital Comparator
circuit. Digital or Binary Comparators are made up from standard AND, NOR
and NOT gates that compare the digital signals present at their input terminals and produce an
output depending upon the condition of those inputs.
For example, along with being able to add and subtract binary numbers we need to be able to compare them
and determine whether the value of input A is greater than, smaller than or equal to the value at
input B etc. The digital comparator accomplishes this using several logic gates that operate on the
principles of Boolean algebra. There are two main types of Digital Comparator available and these are.
- 1. Identity Comparator - an Identity Comparator is a digital comparator that has
only one output terminal for when A = B either "HIGH" A = B = 1
or "LOW" A = B = 0
- 2. Magnitude Comparator - a Magnitude Comparator is a type of digital comparator
that has three output terminals, one each for equality, A = B greater than,
A > B and less than A < B
The purpose of a Digital Comparator is to compare a set of variables or unknown numbers,
for example A (A1, A2, A3, .... An, etc) against that of a constant or unknown value such as
B (B1, B2, B3, .... Bn, etc) and produce an output condition or flag depending upon the result
of the comparison. For example, a magnitude comparator of two 1-bits, (A and B)
inputs would produce the following three output conditions when compared to each other.
Which means: A is greater than B,
A is equal to B, and A is less than
This is useful if we want to compare two variables and want to produce an output when any of the above three
conditions are achieved. For example, produce an output from a counter when a certain count number is reached. Consider the
simple 1-bit comparator below.
1-bit Digital Comparator
Then the operation of a 1-bit digital comparator is given in the following Truth Table.
|B||A||A > B||A = B||A < B|
You may notice two distinct features about the comparator from the above truth table. Firstly, the circuit
does not distinguish between either two "0" or two "1"'s as an output A = B is produced when they
are both equal, either A = B = "0" or A = B = "1". Secondly, the output
condition for A = B resembles that of a commonly available logic gate, the
Exclusive-NOR or Ex-NOR function (equivalence) on each of the
Q = A ⊕ B
Digital comparators actually use Exclusive-NOR gates within their design for
comparing their respective pairs of bits. When we are comparing two binary or BCD values or variables against each other,
we are comparing the "magnitude" of these values, a logic "0" against a logic "1" which is where the term
Magnitude Comparator comes from.
As well as comparing individual bits, we can design larger bit comparators by cascading together
n of these and produce a n-bit comparator just as we did for the
n-bit adder in the previous tutorial. Multi-bit comparators can be constructed to compare
whole binary or BCD words to produce an output if one word is larger, equal to or less than the other.
A very good example of this is the 4-bit Magnitude Comparator. Here, two 4-bit words
("nibbles") are compared to each other to produce the relevant output with one word connected to inputs
A and the other to be compared against connected to input B as shown
4-bit Magnitude Comparator
Some commercially available digital comparators such as the TTL 74LS85 or CMOS 4063 4-bit
magnitude comparator have additional input terminals that allow more individual comparators to be "cascaded"
together to compare words larger than 4-bits with magnitude comparators of "n"-bits being produced. These
cascading inputs are connected directly to the corresponding outputs of the previous comparator as shown
to compare 8, 16 or even 32-bit words.
8-bit Word Comparator
When comparing large binary or BCD numbers like the example above, to save time the comparator
starts by comparing the highest-order bit (MSB) first. If equality exists, A = B then it compares
the next lowest bit and so on until it reaches the lowest-order bit, (LSB). If equality still exists then the two numbers
are defined as being equal.
If inequality is found, either A > B or
A < B the relationship between the two numbers is determined and the comparison
between any additional lower order bits stops. Digital Comparator are used widely in Analogue-to-Digital
converters, (ADC) and Arithmetic Logic Units, (ALU) to perform a variety of arithmetic operations.