Page 11 - Math_Genius_1 2

ckbujh vad osQoy 0 vkSj 1 ls feydj curk gSA ckbujh vad dk mnkgj.k % 110100 gSA ckbujh esa dksbZ 2] 3] 4]
5] 6] 7] 8 ;k 9 ugha gS!

uke (Names) vkdkj (fcV~l) [Size (bits)] mnkgj.k (Examples)

fcV (Bit) 1 ,dy vad ;k rks 0 ;k 1

fucy (Nibble) 4 4 vadksa dk lewg ;k rks 0 ;k 1
ckbV (Byte) 8 8 vadksa dk lewg ;k rks 0 ;k 1

oMZ (Word) 16 16 vadksa dk lewg ;k rks 0 ;k 1

;fn fdlh ckbujh la[;k dk vafre vad 1 gS] rks og la[;k fo"ke gksrh gS_ ;fn ;g 0 gS] rks la[;k le gSA mnkgj.k
osQ fy,µ 1101 ,d fo"ke la[;k rsjg (13) dk çfrfuf/Ro djrk gS_ 10010 ,d le la[;k vV~Bkjg (18) dk
çfrfuf/Ro djrk gSA vkb,] lcls igys ckbujh uacj cukuk lh•saA

pw¡fd ckbujh vad iz.kkyh esa nks vad 0 vkSj 1 gksrs gSa] blfy, bldk vk/kj 2 gksrk gSA ckbujh vad iz.kkyh esa çR;sd
vad ;k fcV 0 ;k 1 gks ldrk gSA ckbujh vadksa osQ la;kstu dk mi;ksx fofHkUu ek=kkvksa tSls 1001 dk çfrfuf/Ro
djus osQ fy, fd;k tk ldrk gSA LFkkuh; ckbujh vad esa çR;sd vad dk ewY; mlosQ nkfgus rjiQ osQ vad osQ LFkkuh;
ewY; ;k vafdr ewY; dk nksxquk gksrk gSA çR;sd LFkku dk Hkkj ?kkr 2 (Power of 2) gSA

LFkku vkSj Hkkj osQ vuqlkj vadksa dk LFkkuh; eku bl çdkj gS %

LFkku (Position) 3 2 1 0 &1 &2
•
Hkkj (Weights) 2 3 2 2 2 1 2 0 2 &1 2 &2

vkWDVy vad iz.kkyh (Octal Number System)
vkWDVy vad iz.kkyh esa 0 ls 7 rd vkB vad gksrs gSaA blfy,] vkWDVy vad iz.kkyh dk vk/kj 8 gSA bl ç.kkyh esa]
çR;sd vad dh fLFkfr 8 osQ ?kkr (Power) dk çfrfuf/Ro djrh gSA bl ç.kkyh esa dksbZ Hkh vad ges'kk 8 ls de
gksrk gSA vkWDVy vad iz.kkyh dk mi;ksx yach ckbujh la[;kvksa osQ 'kkWVZgSaM çfrfuf/Ro osQ :i esa fd;k tkrk gSA la[;k
(841) bl vad ç.kkyh esa ekU; ugha gS D;ksafd 8 ,d ekU; vad ugha gSA
8
gsDlkMsfley vad iz.kkyh (Hexadecimal Number System)
gsDlkMsfley vad iz.kkyh esa 0 ls 9 vkSj , ls ,iQ rd 16 vad gksrs gSaA vYiQkcsV , ls ,iQ 10 ls 15 rd Msfley
la[;k dk çfrfuf/Ro djrs gSaA bl la[;k ç.kkyh dk vk/kj 16 gSA gsDlkMsfley vad iz.kkyh esa çR;sd vad dh fLFkfr

?kkr 16 dk çfrfuf/Ro djrh gSA la[;k (764) oS/ gsDlkMsfley la[;k gSA ;g (764) ls fHkUu gS tks lkr lkS
16
10
pkSalB gSA ;g vad iz.kkyh yach ckbujh la[;kvksa dk çfrfuf/Ro djus osQ fy, 'kkWVZdV fof/ çnku djrh gSA

vad iz.kkyh :ikarj.k (Number System Conversion)
fdlh Hkh vad ç.kkyh dh la[;k dks vU; esa ifjofrZr fd;k tk ldrk gS tSls n'keyo la[;k dks ckbujh la[;k esa
ifjofrZr fd;k tk ldrk gS vkSj blh rjg vU; dks HkhA

Msfley ls ckbujh vad iz.kkyh (Decimal to Binary Number System)
Msfley dks ckbujh la[;k esa cnyus osQ fy,] bu LVsIl dk ikyu djsa %
LVsi 1 n'keyo vad dks 2 ls foHkkftr djsa (ckbujh vad iz.kkyh dk vk/kj)A
LVsi 2 HkkxiQy vkSj 'ks"k dks uksV dj ysaA

vad iz.kkyh 9