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.

**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.

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

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.

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 Comparator**

Then the operation of a 1-bit digital comparator is given in the
following Truth Table.

**Truth Table**

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 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 n-bits giving: 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 below.

**4-bit Magnitude Comparator**

Some commercially available digital comparators such as the TTL
7485 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.

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Basic Electrical and Electronics Engineering : Digital Electronics : The Digital Comparator |

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