Method of translating Boolean algebra into basic algebra

• US 6,959,314 B1
• Filed: 05/13/2002
• Issued: 10/25/2005
• Est. Priority Date: 05/13/2002
• Status: Expired due to Fees

• Current Assignee: Eurica Califorrniaa
• Original Assignee: Eurica Califorrniaa
• Inventors: Califorrniaa, Eurica
• Primary Examiner(s): Ngo, Chuong D
• Application Number:
  US10/145,189
• Time in Patent Office: 1,261 Days
• Field of Search: 708/200, 708/204, 716/3
• US Class Current: 708/200
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544
• CPC Class Codes: G06F 30/30 Circuit design

Abstract

Substituting words written in basic algebra for equivalent words written in Boolean algebra so as to translate Boolean algebra into basic algebra; more generally, summing combinational identity functions factored by their corresponding output values to convert a gate table into basic algebra. The resulting expressions of basic algebra can be simplified and evaluated in the usual straightforward manner.

Claims

1. A method implemented by a computer for translating Boolean algebra into basic algebra, comprising:

(a) assigning signal values s₀ and s₁ to variables, preferably {s₀,s₁}={0,1}; and

(b) substituting respectively the words “

s₀+(a−

s₀)(b−

s₀)/(s₁−

s₀)”

, “

s₁−

(a−

s₁)(b−

s₁)/(s₁−

s₀)”

, and “

s₀+s₁−

a”

written in basic algebra for the words “

intersection of A and B”

, “

union of A and B”

, and “

complement of A”

written in Boolean algebra, so as to translate expressions of Boolean algebra into expressions of basic algebra, which can then be simplified and evaluated in the usual straightforward manner.

2. A method implemented by a computer for converting gate tables into basic algebra, comprising:

(a) assigning a signal identity function for each input data entry in a given row of a gate table as required to assign a combinational identity function for the given row in step (b);

(b) assigning a combinational identity function and factoring it by its corresponding output value for each row of input data in the gate table; and

(c) summing combinational identity functions factored by their corresponding output values for each row in the gate table.

3. A shortcut method implemented by a computer for converting gate tables with binary output into basic algebra, comprising:

(a) assigning a signal identity function for each input data entry in a given row of a gate table as required to assign a combinational identity function for the given row in step (b);

(b) assigning a combinational identity function either for each row of input data in the gate table with output so or for each row with output s₁; and

(c) summing combinational identity functions either for rows in the gate table with output s₀ or for rows with output s₁, such that if rows with output s₀ are selected, the sum is factored by the quantity (s₀−

s₁) and s₁ is added to the result, or if rows with output s₁ are selected, the sum is factored by the quantity (s₁−

s₀) and s₀ is added to the result.