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Page 10 - Math_Genius_1 2
P. 10

    la[;k ç.kkfy;k¡ pkj çdkj dh gksrh gSa tks bl çdkj gSa%
                          1-  n'keyo vad iz.kkyh                             3-  vkWDVy vad iz.kkyh

                          2-  ckbujh vad iz.kkyh                             4-  gsDlkMsfley vad iz.kkyh
                      n'keyo vad ç.kkyh lkekU; :i ls ç;ksx dh tkrh gSA gkyk¡fd] oaQI;wVj ckbujh vad iz.kkyh dk mi;ksx djrs gSaA
                      oaQI;wVj esa vkWDVy vkSj gsDlkMsfley la[;k iz.kkyh dk Hkh mi;ksx fd;k tkrk gSA

                      n'keyo vad iz.kkyh (Decimal Number System)
                      n'keyo vad iz.kkyh la[;kvksa dks n'kkZus osQ fy, ,d ekud vad ç.kkyh gSA blesa 0 ls 9 rd nl vad gksrs gSaA
                      n'keyo vad iz.kkyh esa fdlh Hkh la[;kRed eku dk çfrfuf/Ro djus osQ fy, osQoy bu vadksa dk mi;ksx fd;k tk
                      ldrk gSA blfy,] n'keyo vad iz.kkyh dk vk/kj 10 gSA n'keyo vad iz.kkyh lcls O;kid :i ls mi;ksx dh
                      tkus okyh la[;k ç.kkyh gSA bafMfotqvy fMftV (Individual digit) n~okjk n'kkZ;k x;k eku vad osQ Hkkj (Weight)
                      vkSj LFkku (Position) ij fuHkZj djrk gSA

                      n'keyo fcanq osQ ckb± vksj igys vad dh fLFkfr 0 gSA n'keyo fcanq osQ ckb± vksj nwljs vad dh fLFkfr 1 gSA blh
                      rjg] n'keyo fcanq osQ nkb± vksj igys vad dh fLFkfr &1 gSA n'keyo fcanq osQ nkb± vksj nwljs vad dh fLFkfr &2 gS]
                      vkSj blh rjgA
                      fdlh la[;k dk eku vadksa dks muosQ LFkku osQ Hkkj ls xq.kk djosQ vkSj ifj.kke tksM+dj fu/kZfjr fd;k tkrk gSA bl fof/

                      dks foLrkj fof/ (expantion method) osQ :i esa tkuk tkrk gSA la[;k osQ lcls nkfgus vad dk Hkkj (Weight)
                      lcls de gksrk gSA bl vad dks yhLV flfXufiQosaQV fMftV (,y,lMh/Least Significant Digit/LSD)) dgk
                      tkrk gSA fdlh la[;k osQ lcls ck,¡ vad dk Hkkj lcls vf/d gksrk gSA bl vad dks eksLV flfXufiQosaQV fMftV

                      (,e,lMh) (Most Significant Digit-MSD) dgk tkrk gSA la[;k 724 esa vad 7 lcls egRoiw.kZ vad gS vkSj 4
                      lcls de egRoiw.kZ vad gSA
                      fuEu rkfydk n'keyo la[;k (724)  dk fLFkuh; Hkkj n'kkZrh gSA
                                                      10

                                                              lSdM+k  (Hundreds)     ngkbZ  (Tens)     bdkbZ  (Units)

                                   Hkkj  (Weights)                    10 2                10 1              10 0
                           izR;sd la[;k dk okLrfod ewY;            7 × 10  2           2 × 10  1         4 × 10  0
                             (Real Value of Each Digit)

                                  ifj.kke  (Result)                  700                  20                 4

                      ckbujh vad iz.kkyh (Binary Number System)
                      ckbujh 'kCn ^ckbZ&* (bi-) ls vk;k gS] ftldk vFkZ gSµ nksA ge ^ckbZ&* (bi-) dks ^ckbfldy* (bicycle) (nks
                      ifg,) ;k ^nwjchu* (binocularµnks vk¡•sa) tSls 'kCnksa esa ns•rs gSaA ckbujh vadksa dk vk/kj 2 gksrk gSA

                        vkvks tkusa!

                         ,d ,dy ckbujh vad (single binary digit) (tSls ^0* ;k ^1*) dks ^fcV* (bit) dgk tkrk gSA mnkgj.k osQ fy,
                         11010 ik¡p fcV yack gSA fcV 'kCn ^ckbujh fMftV* (binary digit) 'kCnksa ls cuk gSA

                      oaQI;wVj ,d e'khu gS] tks VªkaftLVlZ] fLop vkSj vU; ?kVdksa (Components) ls cuh gksrh gSA ;s lHkh bysDVªkWfud
                      ?kVd nks ijLij vuU; (mutually exclusive) voLFkkvksa esa gSa] ;k rks vkWu ;k vkWiQA nks ckbujh vad bu nks voLFkkvksa
                      dk çfrfuf/Ro djrs gSaA oaQI;wVj dks fn, x, çR;sd funZs'k dks 0 vkSj 1 esa cny fn;k tkrk gS rkfd bls oaQI;wVj }kjk

                      le>k vkSj dk;kZfUor fd;k tk losQA blfy, ckbujh Hkk"kk dks e'khuh Hkk"kk osQ :i esa tkuk tkrk gSA

                         8   Play (Ver. 1.0)-VII

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