Calculation Apparatus Zero Correction for Significant Digit Cancellation

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Solution Overview

Problem

Conventional calculation apparatuses face issues with maintaining arithmetic precision, particularly in subtractions between equivalent or close numerals, leading to errors due to cancellation of significant digits and subsequent propagation of errors in calculations.

Innovation Solution

A calculation apparatus with an input device, calculator, detection unit, and zero correction unit that corrects results to zero when predetermined upper digits are zero, and adjusts the least significant digit when significant digit cancellation occurs, ensuring accurate results and minimizing rounding-off errors.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If a large number of digits are used for floating point operation, then measurement precision is improved, but significant digits are cancelled in subtraction between equivalent or close numerals

Engineering Contradiction:

Improvearithmetic precisionVSAvoidsignificant digits

Core Design Contradiction:

Measurement precisionVSLoss of information

Solution Approach 1:

The patent performs a preliminary check on the calculation result before final output. When a subtraction operation yields a result where all significant digits are cancelled (result is zero or extremely close to zero), the system proactively identifies this condition and applies corrective action by setting the result to zero, preventing the propagation of meaningless precision errors in subsequent calculations.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent converts the harmful effect of significant digit cancellation into a beneficial outcome. By detecting when significant digits are cancelled and intentionally setting the result to zero, the system transforms what would normally be a precision error into an accurate representation of the mathematical reality, thereby improving overall calculation reliability.

Inventive Principle:

Principle #22Blessing in disguise (Convert harm into benefit)

2Measurement precision

If rounding-off correction is performed using higher precision results, then measurement precision is improved, but calculation time increases

Engineering Contradiction:

Improvecalculation accuracyVSAvoidcalculation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent applies rounding-off correction selectively rather than universally. The system performs higher precision calculation and rounding-off correction only for specific operations where it is most beneficial (such as subtraction operations prone to significant digit cancellation), while maintaining standard precision for other operations, thereby optimizing the balance between accuracy and computation time.

Inventive Principle:

Principle #3Local quality

Data Source

PatentUS7941473B2Calculation apparatus and storage medium in which calculation program is stored

Publication Date: 2011.05.10 CASIO COMPUTER CO LTD

AI summary

In a graphing calculator, a decimal calculation unit obtains a calculation result of an arithmetic expression input by an input device to an n-th digit and an (n+m)-th digit. When the values from the most significant digit to an (n+1)-th digit in the (n+m)-digit calculation result are zero, with respect to an addition or subtraction, the CPU corrects an n-digit calculation result of the addition or subtraction to zero.