Associative Memory Binary Number Comparison
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Solution Overview
Problem
Long division of large binary numbers is computationally expensive due to the need for multiple subtraction operations, which increases complexity as the size of the numbers grows, especially when using traditional methods like long division algorithms.
Innovation Solution
The method involves replacing the subtraction operation in long division with an addition operation using the two's complement representation of the denominator, performed on an associative memory device, which allows for concurrent processing and prediction of carry bits without actual summation, reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional long division algorithm is used, then division operation can be performed, but computational complexity increases as O(n*d) due to multiple subtraction operations
Solution Approach 1:
The patent replaces the mechanical subtraction operation with an optical comparison process. The associative memory array optically compares the partial remainder with the divisor simultaneously across all bit positions, eliminating the need for sequential subtraction operations. This optical comparison approach reduces the complexity from O(n*d) to O(n) by performing the comparison in parallel rather than through multiple sequential mechanical subtraction steps.
2Measurement precision
If multiple subtraction operations are performed, then accurate quotient and remainder are obtained, but processing time increases significantly for large numbers
Solution Approach 1:
The patent performs preliminary setup by loading the divisor and its two's complement into the associative memory array before the division process begins. This preliminary action enables the subsequent comparison operations to proceed rapidly without repeated setup overhead, significantly reducing the total processing time for large number division while maintaining accuracy through the pre-configured memory structure.
Solution Approach 2:
The patent substitutes the time-consuming sequential subtraction process with a parallel optical comparison mechanism. The associative memory array simultaneously compares bits across all positions, determining quotient bits in parallel rather than sequentially, thereby dramatically reducing processing time while preserving division accuracy.
3Reliability
If sequential bit processing is used, then correct division result is achieved, but the process becomes increasingly expensive computationally as numbers grow larger
Solution Approach 1:
The patent transitions from sequential one-dimensional bit processing to parallel two-dimensional processing by utilizing the associative memory array's row-column structure. Multiple bits are processed simultaneously across different rows and columns, effectively adding a spatial dimension to the computation. This dimensional change enables parallel processing that reduces computational expense from O(n*d) to O(n) while maintaining result correctness through systematic processing of all bit positions.
Data Source
AI summary
A method to compare between a first number and a second number includes the steps of storing the first number in a first row of an associative memory array, storing a two's complement representation of the second number in a second row of the associative memory array wherein bit i of the second number is stored in a same column of the associative memory array as bit i of the first number, concurrently performing a carry save operation on a plurality of columns of the associative memory array to create a sum and a carry, predicting a value of a carry out bit without adding the sum and the carry, and indicating that the first number is smaller than the second number if the value of the carry out bit is 1.