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Technique for Evaluating Square Roots

IP.com Disclosure Number: IPCOM000096206D
Original Publication Date: 1963-Feb-01
Included in the Prior Art Database: 2005-Mar-07
Document File: 3 page(s) / 18K

Publishing Venue

IBM

Related People

Meggitt, JE: AUTHOR

Abstract

Square roots can be evaluated by an electronic computer by the following procedure which is demonstrated by a sample calculation. Problem: Evaluate sqrt 1156 Calculation: Step 1 Multiply radicand by 5 (to obtain 5780). This is achieved by moving the decimal point one position to the right and dividing by 2. Step 2 Partition the multiplied radicand into pairs of digits, counting from the decimal point, and sequentially subtract the odd multiples of 5 from the highest order partition, until no more subtraction with a positive remainder is possible.

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Technique for Evaluating Square Roots

Square roots can be evaluated by an electronic computer by the following procedure which is demonstrated by a sample calculation. Problem: Evaluate sqrt 1156

Calculation: Step 1 Multiply radicand by 5 (to obtain 5780). This is

achieved by moving the decimal point one position

to the right and dividing by 2.

Step 2 Partition the multiplied radicand into pairs of digits,

counting from the decimal point, and sequentially

subtract the odd multiples of 5 from the highest

order partition, until no more subtraction with a

positive remainder is possible. This is shown as

follows:

5780 5

-5

52 15

-15

37 25

-25

12 35

Step 3 Operate on the remainder followed by the next pair

of digits (1280) by sequentially subtracting odd

multiples of 5, beginning with the multiple (305)

that is obtained from the first multiple of 5 that

is not used in step 2 (35) by shifting the tens digit

(3) (and higher-order digits, if any) to the left

one position, as follows:

1280 305

-305

975 315

-315

660 325

-325

335 335

-335

0 345

Step 4 Repeat step 3 until all digits of the multiplied

radicand are exhausted or until the desired degree of

accuracy is obtained. The square root 34 is

represented by the higher-order digits of the first

multiple of 5 that is not used in the last step.

This procedure has several advantages over the square root technique which employs subtraction of successive odd numbers in that:

1. The result is provided by the circuit that genera...