Written calculation engineering scheme of carry line digital engineering method in increasing Q scale
Written calculation engineering scheme of carry line digital engineering method in increasing Q scale
 CN 1,760,825 A
 Filed: 09/30/2005
 Published: 04/19/2006
 Est. Priority Date: 09/30/2004
 Status: Active Application
First Claim
1. a written calculation engineering technical scheme that increases Q system, carry line number digit engineering method adopts Q system number, counts computing with the Q system;
 It is characterized in that, adopt " increasing the Q system " number, with " mixing number system, carry row method " computing;
Chinese PRB Reexamination
Abstract
The disclosed method increases calculation speed remarkably, and lowers error rate of written calculations greatly. The method includes following steps: converting K pieces of number participating to adding and subtracting calculation in common Q scale to K or 2K pieces of number in increasing Q scale; next, carrying out summation for K or 2K pieces of number under increasing Q scale; carrying out XOR operation starting from least significant bit or each bit at same time, and logging sum to next operation layer; at same time, depositing the carry obtained in increasing Q scale to next calculation layer, or space bit of high power adjacent to any not calculated data column in this calculation layer or zero bit. Calculation is such carried out that till only one number is obtained in calculation layer. The final number is the sum of addition in increasing Q scale.
10 Claims

1. a written calculation engineering technical scheme that increases Q system, carry line number digit engineering method adopts Q system number, counts computing with the Q system;
 It is characterized in that, adopt " increasing the Q system " number, with " mixing number system, carry row method " computing;
 It is characterized in that, adopt " increasing the Q system " number, with " mixing number system, carry row method " computing;

2. increase the written calculation engineering technical scheme of Q system, carry line number digit engineering method as claim 1, it is characterized in that, " mixing number system, carry row method " computing can be one of following scheme;
 Scheme one;
(being suitable in computing machine, the written calculation engineering) be common Q system number encoder or be converted to separately and mix number system numbers 1.;
2. mix number system computing (" liquidating ", " drawing Q ", " adding up ");
3. mix the number decoding of number system or be converted to common Q system number separately;
Scheme two;
(be suitable in computing machine, the abacus;
Also can be used for written calculation engineering, also can;
) 1. common Q system number encoder or be converted to separately and mix number system numbers;
Mixing number system number encoder is " the full system number of encoding ";
2. " the full system number of encoding " computing (" liquidating ", " drawing Q ", " adding up ");
3. " the full system number of encoding " is decoded as and mixes number system number;
Mix the number decoding of number system or be converted to common Q system number separately;
Scheme three;
(being suitable in the computing machine) be common Q system number encoder or be converted to separately and mix number system numbers 1.;
Mix number system number encoders or be converted to separately 0, ±
1} binary number (its special condition is " an ordinary binary number ");
2. 0, ±
1} binary arithmetic (" liquidating ", " drawing Q ", " adding up ");
3. { 0, ±
1} binary number is deciphered or is converted to separately to mix and counts the system number;
Mix the number decoding of number system or be converted to common Q system number separately;
Scheme four;
(being suitable in the computing machine) be common Q system number encoder or be converted to separately and mix number system numbers 1.;
Mix number system number encoders or be converted to " coding { 0, ±
1} binary number " (its special condition be " ordinary binary of an encoding number ") separately;
2. " coding 0, ±
1} binary number " computing (" liquidating ", " drawing Q ", " adding up ");
3. " coding 0, ±
1} binary number " decipher or be converted to separately to mix and count the system number;
Mix the number decoding of number system or be converted to common Q system number separately;
Among the present invention, employing scheme one, scheme two are showed.
 Scheme one;

3. increase the written calculation engineering technical scheme of Q system, carry line number digit engineering method as claim 12, it is characterized in that, " mixing number system, carry row method " comprises following first kind of step:

The 1st step, establish K common Q system number and participate in plus and minus calculation, K is 〉
=2 integer, Q is a natural number;
These number conversions are become K or the individual Q system number that increases of 2K;
(among the present invention, all adopt 2K to increase Q system number and show);In the 2nd step,, increase the summation operation of Q system to two numbers in K or the 2K number;
Begin or every addition of stepbystep simultaneously from lowest order, promptly on a certain position, get this two numbers stepbystep addition;
Adopt " liquidating ", " drawing Q ", add up, obtain this this position of two numbers " addition without carry " and number;
This and number scale are gone into next operation layer, as " partly and " number;
Simultaneously gained " increases the Q carry ", then is stored in the not computing as yet of next operation layer or this operation layer, the room of the adjacent high position of arbitrary data line or 0 place;In the 3rd step, on an adjacent high position of abovementioned certain, repeat the computing in the 2nd step;
So repeatedly, till the also own computing of two number most significant digits;
When adopting concurrent operation, everybody carries out the 2nd step and the 3rd step computing simultaneously two numbers, and then this step can jump over over;The 4th step, get two numbers in addition in K or the 2K number, carry out the 2nd step and the 3rd step computing;
So repeatedly, till all number average has been got in K or 2K number exclusive disjunction layer;
When a remaining number only, then directly move to next operation layer as " partly and " number;In the 5th step, in next operation layer, abovementioned " stepbystep and " number and " carry " number are carried out aforementioned the 2nd step, the 3rd step, the 4th step summation operation;
So repeatedly, in operation layer, only obtain till the number after the computing;
Then last gained increases additive operation of Q system and number, is the K that asks common Q system and counts the plus and minus calculation result;Perhaps, adopt following second kind of step; The 1st step, establish K common Q system number and participate in plus and minus calculation, K is 〉
=2 integer, Q is a natural number;
These number conversions are become K or the individual Q system number that increases of 2K;
(among the present invention, all adopt 2K to increase Q system number and show);In the 2nd step,, promptly on a certain position, get two numbers, K or the addition simultaneously of 2K number from lowest order;
Adopt " liquidating ", " drawing Q ", add up;
Promptly when two numbers, obtain this position of two numbers " addition without carry " and number;
This and number scale are gone into next operation layer, as " partly and " number;
Simultaneously gained " increases the Q carry ", then is stored in the not computing as yet of next operation layer or this operation layer, the room of the adjacent high position of arbitrary data line or 0 place;The 3rd step, on abovementioned certain position, get two numbers in addition in K or the 2K number, repeat the computing in the 2nd step;
So repeatedly, till all number average has been got in K or 2K number exclusive disjunction layer;
When a remaining number only, then directly move to next operation layer as " partly and " number;When adopting same position to go up each number computing simultaneously, carry out the 2nd step and the 3rd step computing simultaneously, then this step can jump over over;
At this moment on same position, to n be that 0 number carries out " liquidating " earlier;
Then, carry out " stroke Q " to n with for the number of mQ;
N is 〉
=2 integer, and m is an integer;
Gained " increases the Q carry ", then is stored in the not computing as yet of next operation layer or this operation layer, the room of the adjacent high position of arbitrary data line or 0 place;
On the same position, remaining each number carries out " adding up ", perhaps directly moves to next operation layer;
Add up " majority adds up " of employing 〉
=2;
When adopting common two to count " adding up ", then the order serial adds up;In the 4th step, on an adjacent high position of abovementioned certain, repeat the computing in the 2nd step and the 3rd step;
So repeatedly, until K or 2K number most significant digit also till the computing;In the 5th step, in next operation layer, abovementioned " stepbystep and " number and " carry " number are carried out aforementioned the 2nd step, the 3rd step, the 4th step summation operation;
So repeatedly, in operation layer, only obtain till the number after the computing;
Then last gained increases additive operation of Q system and number, is the K that asks common Q system and counts the plus and minus calculation result;Perhaps, adopt following the third step; The 1st step, establish K common Q system number and participate in plus and minus calculation, K is 〉
=2 integer, Q is a natural number;
These number conversions are become K or the individual Q system number that increases of 2K;
(among the present invention, all adopt 2K to increase Q system number and show);In the 2nd step, adopt socalled " twodimentional computing ";
That is, on everybody of K or 2K number, carry out computing simultaneously;
And simultaneously on each, n and be that 0 number carries out " liquidating ";
N is 〉
=2 integer;In the 3rd step, adopt socalled " twodimentional computing ";
That is, on everybody of K or 2K number, carry out computing simultaneously;
And simultaneously on each, n and carry out " stroke Q " for the number of mQ;
N is 〉
=2 integer, and m is an integer;
Gained " increases the Q carry ", then is stored in next operation layer, the room of the adjacent high position of arbitrary data line or 0 place;In the 4th step, adopt socalled " twodimentional computing ";
That is, on everybody of K or 2K number, carry out computing simultaneously;
And simultaneously on each, remaining each number carries out " adding up ", perhaps directly moves to next operation layer;
Add up " majority adds up " of employing 〉
=2;
When adopting common two to count " adding up ", then the order serial adds up;In the 5th step, in next operation layer, abovementioned " stepbystep and " number and " carry " number are carried out aforementioned the 2nd step, the 3rd step, the 4th step summation operation;
So repeatedly, in operation layer, only obtain till the number after the computing;
Then last gained increases additive operation of Q system and number, is the K that asks common Q system and counts the plus and minus calculation result.


4. increase the written calculation engineering technical scheme of Q system, carry line number digit engineering method as claim 13, it is characterized in that, " carry row method " adopted in " mixing number system, carry row method " computing;
 In calculating process, the carry that produces is left in the adjacent high position " carry row ", carry out computing with " stepbystep and " then.

5. increase the written calculation engineering technical scheme of Q system, carry line number digit engineering method as claim 14, it is characterized in that, " mix number system, carry row method " when the n number in the K number is carried out summation operation, if on a certain position, the addition without carry of n operand and be zero wherein, but produce carry m (with the n number consistent) with numerical symbol;
 N is 〉
=2 integer, and m is an integer;
Carry is put into the not computing as yet of next operation layer or this operation layer, the room of the adjacent high position of arbitrary data line or 0 place;
Then, with certain all reset logically of position of n operand, no longer participate in later computing;
This is called " drawing Q ";
During m=0, be called " liquidating " in " draw Q ";
Perhaps, do not adopt " liquidating " to reach " drawing Q ".
 N is 〉

6. increase the written calculation engineering technical scheme of Q system, carry line number digit engineering method as claim 15, it is characterized in that, " mixing number system, carry row method " can not encode;
 Can mix several system number encoders;
Also can complete one yard encode, be about to each and increase each figure place S of Q system number, all arrange come corresponding from the lowest order order to highorder with  S 1, all the other high positions are 0, and total bit then is Q/2 or (Q+1)/2;
Simultaneously, with the number symbol of S, the number of promptly representing this is a plus or minus, as the number symbol on each in corresponding complete a yard;
When adopting complete one yard to encode when increasing the Q system and counting, n number addition only is 1 or 1 a not repeated arrangement in the n number;
Its complete one yard compiling can be decided code length or become code length.
 Can mix several system number encoders;

7. increase the written calculation engineering technical scheme of Q system, carry line number digit engineering method as claim 16, it is characterized in that:
 the written calculation engineering technical scheme adopts " increasing Q system, carry row method " computing, and Q is a natural number;
In the written calculation engineering of the present invention, mix the computing of number system and can be aforementioned schemes one or scheme two;
Now adopt scheme one to show;
If K common Q system number participated in plus and minus calculation, K is 〉
=2 integer, and Q is a natural number;
These number conversions are become K or the individual Q system number that increases of 2K;
(among the present invention, all adopt 2K to increase Q system number and show);
Digital engineering method in the written calculation engineering can adopt aforementioned first kind or second kind of step;
Here, adopt second kind of step to show.
 the written calculation engineering technical scheme adopts " increasing Q system, carry row method " computing, and Q is a natural number;

8. increase the written calculation engineering technical scheme of Q system, carry line number digit engineering method according to claim 17, it is characterized in that:
 when the written calculation engineering technical scheme is carried out summation operation to the n number in the K number, if on a certain position, the addition without carry of n operand and be zero wherein, but produce carry m (with the n number consistent) with numerical symbol;
N is 〉
=2 integer, and m is an integer;
Carry is put into the not computing as yet of next operation layer or this operation layer, the room of the adjacent high position of arbitrary data line or 0 place;
Then, with certain all reset logically of position of n operand, no longer participate in later computing;
This is called " drawing Q ";
During m=0, be called " liquidating " in " draw Q ";
Perhaps, do not adopt " liquidating " to reach " drawing Q ".
 when the written calculation engineering technical scheme is carried out summation operation to the n number in the K number, if on a certain position, the addition without carry of n operand and be zero wherein, but produce carry m (with the n number consistent) with numerical symbol;

9. increase the written calculation engineering technical scheme of Q system, carry line number digit engineering method according to claim 18, it is characterized in that:
 the described operand of written calculation engineering technical scheme can not encoded;
Can mix several system number encoders;
Also can complete one yard encode, be about to each and increase each figure place S of Q system number, all arrange come corresponding from the lowest order order to highorder with  S 1, all the other high positions are 0, and total bit then is Q/2 or (Q+1)/2;
Simultaneously, with the number symbol of S, the number of promptly representing this is a plus or minus, as the number symbol on each in corresponding complete a yard;
When adopting complete one yard to encode when increasing the Q system and counting, n number addition only is 1 or 1 a not repeated arrangement in the n number;
Complete one yard compiling can be decided code length or become code length;
The present invention increases in Q system, the carry row written calculation engineering, adopts the change code length to show.
 the described operand of written calculation engineering technical scheme can not encoded;

10. increase the written calculation engineering technical scheme of Q system, carry line number digit engineering method according to claim 19, it is characterized in that:
 the wherein said operand of written calculation engineering technical scheme is to increase Q system number, and Q is a natural number.
Specification(s)