Page 13 - Math_Genius_1 2

vkWDVy ls n'keyo :ikarj.k (Octal to Decimal Conversion)
ckbujh uacj osQ leku] vki la[;k osQ çR;sd vad dks nk;ha vksj ls 'kq: gksus okyh 8 dh c<+rh ?kkrksa osQ lkFk xq.kk
djosQ ,d vkWDVy la[;k dks n'keyo la[;k esa ifjofrZr dj ldrs gSaA mnkgj.k osQ fy,&
mnkgj.k û% (37) dks n'keyo esa cnysaA mnkgj.k û% (467) dks n'keyo esa cnysaA
8 8
0
1
1
2
(37) ¾ 3 × 8 $ 7 × 8 (467) ¾ 4 × 8 $ 6 × 8 $ 7 × 8 0
8
8
¾ 24 $ 7 ¾ 4 × 64 $ 6 × 8 $ 7 × 1
(37) ¾ (31) (467) ¾ (311)
8 10 8 10
gsDlkMsfley ls n'keyo :ikarj.k (Hexadecimal to Decimal Conversion)
vki ,d gsDlkMsfley la[;k dks n'keyo la[;k esa ifjofrZr dj ldrs gSa] la[;k osQ çR;sd vad dks 16 dh c<+rh
?kkrksa osQ lkFk xq.kk djosQ nkb± vksj ls 'kq: dj ldrs gSaA mnkgj.k osQ fy,]
mnkgj.k û% (3B) dks n'keyo esa cnysaA mnkgj.k ü% (3A4) dks n'keyo esa cnysaA
16
16
1
2
0
1
3B ¾ 3 × 16 + 11 × 16 (3A4) ¾ 3 × 16 + 10 × 16 + 4 × 16°
16
16
¾ 48 + 11 ¾ 768 + 160 + 4
(3B) ¾ (59) (3A4) ¾ (932)
16 10 16 10
ckbujh vad lapkyu (Operations on Binary Numbers)
xf.kr dh rjg gh] ,d oaQI;wVj flLVe tksM+] ?kVko] xq.ku vkSj foHkktu (Hkkx) tSls ckbujh la[;kvksa ij vyx&vyx
lapkyu dj ldrk gSA

ckbujh tksM+ (Binary Addition)
ckbujh tksM+ n'keyo la[;kvksa osQ ;ksx osQ leku gSA tc tksM+ dk eku 1 eku ls vf/d gks tkrk gS] eku yhft, 10
;k 11] rks 1 dks orZeku fLFkfr osQ ckb± vksj ys tk;k tkrk gSA nks ckbujh vadksa dks tksM+us osQ fu;e uhps fn, x, gSa%

X Y X + Y

0 0 0 + 0 = 0

0 1 0 + 1 = 1

1 0 1 + 0 = 1
1 1 1 + 1 = 10 (gkfly 1)

mnkgj.k osQ fy,] vkb, ge ckbujh uacj (101111) vkSj (10111) tksM+saA
2 2

1 1 1 1 1 µµµ gkfly (Carry) fcV~l

1 0 1 1 1 1
$ 1 0 1 1 1

1 0 0 0 1 1 0

vad iz.kkyh 11