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Date tag: January 25 2010 8:5:59
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Date tag: January 25 2010 8:3:44
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Date tag: January 25 2010 7:59:44
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Date tag: January 25 2010 7:55:58
the 3 theorem.
Date tag: January 25 2010 7:51:3
the 9 theorem
Date tag: January 25 2010 7:48:14
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Date tag: January 25 2010 7:45:25
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Date tag: January 25 2010 7:40:14
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Date tag: January 25 2010 7:36:16
Divisibility tests, the x theorem
Date tag: January 25 2010 7:35:54
Definition of congruence.
Date tag: January 25 2010 6:19:58
We generally prefer 2 level implementations, as they minimize the total delay in computation.
Date tag: January 25 2010 6:19:42
Either a canonical form or a standard form gives rise to a 2 level implementation.
Date tag: January 25 2010 6:16:53
We can also express a function as a sum of products, in which a given product need not be a minterm, or a product of sums where the sums need not be maxterms. These representations are called standard forms. Standard form representations are not unique.
Date tag: January 25 2010 6:9:46
Every boolean function can be represented in either of thses two canonical forms, as a sum of minterms or a product of maxterms. Such a representation is also unique.
Date tag: January 25 2010 6:9:19
Define the complement f prime of a function is the function whose value is always the complement of that function. The product of the maxterms for the rows where f1 is 0, simalarly for f2.
Date tag: January 25 2010 6:4:26
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Date tag: January 25 2010 6:4:15
So every maxterm is false in exactly one row of the truth table. We can find an expression for a given function by summing the minterms associated with the rows of the truth table when the function is true.
Date tag: January 25 2010 5:56:15
Minterms Maxterms
Date tag: January 25 2010 5:53:11
Each minterm is true in exactly 1 row of our truth table. A maxterm is a sum of 3 literals, each containing a different variable. By de Morgans laws every maxterm is the complement of some minterm.
Date tag: January 25 2010 5:45:20
Canonical and standard forms: Suppose were considering a function of 3 boolean variables x y z. A minterm is a product of 3 literals, each containing a different variable.
Date tag: January 25 2010 5:45:11
In expressions like the above, a variable or its complement is called a literal and a product or sum of literals is called a term. Both the number of literals and the number of terms are measures of the complexity of a formula.
Date tag: January 25 2010 5:37:15
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Date tag: January 22 2010 9:19:5
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Date tag: January 22 2010 9:16:41
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Date tag: January 22 2010 9:12:36
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Date tag: January 22 2010 9:9:38
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Date tag: January 22 2010 9:6:16
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Date tag: January 22 2010 9:1:34
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Date tag: January 22 2010 8:58:49
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Date tag: January 22 2010 8:55:35
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Date tag: January 22 2010 8:55:29
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Date tag: January 22 2010 8:55:21
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Date tag: January 22 2010 8:46:7
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Date tag: January 22 2010 8:39:17
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Date tag: January 22 2010 8:35:9
Taylors inequality
Date tag: January 22 2010 8:23:2
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Date tag: January 22 2010 8:19:58
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Date tag: January 22 2010 8:18:42
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Date tag: January 22 2010 8:15:39
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Date tag: January 22 2010 8:10:43
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Date tag: January 22 2010 8:10:25
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Date tag: January 22 2010 8:2:34
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Date tag: January 22 2010 8:0:36
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Date tag: January 22 2010 8:0:23
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Date tag: January 22 2010 7:52:58
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Date tag: January 22 2010 7:47:16
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Date tag: January 22 2010 7:44:4
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Date tag: January 22 2010 7:38:24
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Date tag: January 22 2010 7:33:3
Congruences Let M be a fixed positive integer. For integers a and b we say that a is congruent to be modulo m and write...
Date tag: January 22 2010 6:17:17
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