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| {{other uses|comparator (disambiguation)}}
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| A '''digital comparator''' or '''magnitude comparator''' is a [[Computer hardware|hardware]] electronic device that takes two numbers as input in [[Binary numeral system|binary]] form and determines whether one number is greater than, less than or equal to the other number. Comparators are used in [[central processing unit]] s (CPUs) and [[microcontroller]]s (MCUs). Examples of digital comparator include the CMOS 4063 and 4585 and the TTL 7485 and 74682-'89.
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| Note: X NOR gate is a basic comparator, because its output is "1" only if its two input bits are equal.
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| The [[analog signal|analog]] equivalent of digital comparator is the [[comparator|voltage comparator]]. Many [[microcontroller]]s have analog comparators on some of their inputs that can be read or trigger an [[interrupt]].
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| ==Implementation==
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| Consider two 4-bit binary numbers A and B so
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| <math>A=A_3A_2A_1A_0</math>
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| <math>B=B_3B_2B_1B_0</math>
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| Here each subscript represents one of the digits in the numbers.
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| ;Equality
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| The binary numbers A and B will be equal if all the pairs of significant digits of both numbers are equal, i.e.,
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| <math>A_3=B_3</math>, <math>A_2=B_2</math>, <math>A_1=B_1</math> and <math>A_0=B_0</math>
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| Since the numbers are binary, the digits are either 0 or 1 and the boolean function for equality of any two digits <math>A_i</math> and <math>B_i</math> can be expressed as
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| <math>x_i= A_i \cdot B_i + \overline{A}_i \cdot \overline{B}_i</math>.
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| <math>x_i</math> is 1 ''only if'' <math>A_i</math> and <math>B_i</math> are equal.
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| For the equality of A and B, all <math>x_i</math> variables (for i=0,1,2,3) must be 1.
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| So the quality condition of A and B can be implemented using the [[AND gate|AND]] operation as
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| <math>(A=B) = x_3x_2x_1x_0</math> | |
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| The binary variable (A=B) is 1 only if all pairs of digits of the two numbers are equal.
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| ;Inequality
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| In order to manually determine the greater of two binary numbers, we inspect the relative magnitudes of pairs of significant digits, starting from the [[most significant bit]], gradually proceeding towards lower significant bits until an inequality is found. When an inequality is found, if the corresponding bit of A is 1 and that of B is 0 then we conclude that A>B.
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| This sequential comparison can be expressed logically as:
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| <math>(A>B)=A_3 \cdot \overline{B}_3+x_3 A_2 \overline{B}_2+x_3 x_2 A_1 \overline{B}_1+x_3x_2x_1 A_0 \overline{B}_0</math>
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| <math>(A<B)=\overline{A}_3 \cdot B_3+x_3 \overline{A}_2 B_2+x_3 x_2 \overline{A}_1 B_1+x_3x_2x_1 \overline{A}_0 B_0</math>
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| (A>B) and (A < B) are output binary variables, which are equal to 1 when A>B or A<B respectively.
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| == See also ==
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| *[[4000 series]]
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| *[[7400 series]]
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| * [[Sorting network]]
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| == External links ==
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| *[http://focus.ti.com/general/docs/hirel/hirellanding.tsp?familyId=719&rootFamilyId=698 Digital Comparators by Texas Instruments]
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| [[Category:Digital circuits]]
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