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Page 13 - Math_Genius_1 2
P. 13

    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

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