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
