kxn ami2`m2 2t` b2mi ibqmpqmw ?h2m - uni … · í s cmfi+?2mq#2mu7 c`lkh miv¾ ¾Õ¾Í¾Ì¾ ¾...

58
10 0 10 1 10 2 2 × 10 2 +5 × 10 1 +3 × 10 0 = 253 2 n-1 2 n 1 × 2 0 =1 1 × 2 1 =2 0 × 2 2 =0 1 × 2 3 =8 = 11 b t - x =1+ t-1 i=0 (b - 1) × b i - t-1 i=0 a i × b i =1+ t-1 i=0 (b - 1 - a i ) × b i

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Page 1: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾

100

101

102

2× 102 + 5× 101 + 3× 100 = 253

2n−1

2n

1× 20 = 11× 21 = 20× 22 = 01× 23 = 8

= 11

bt− x = 1 +

t−1i=0 (b− 1)× bi

−∑

t−1i=0 ai × bi = 1 +

t−1i=0 (b− 1− ai)× bi

Page 2: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾

−4 = 100−3 = 101−2 = 110−1 = 111

0 = 0001 = 0012 = 0103 = 011

x = m× be, e ∈ N

5, 5× 103 5, 5 3

2× 82 + 1× 81 + 0× 80 = 21053 = 65 = 6× 81 + 5× 80

53 = 77 = 7× 81 + 7× 80

136 = 210 = 2× 82 + 1× 81 + 0× 80

8× 161 + 8× 160 = 88

16 = 2× 2× 2× 2

Page 3: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾

53 = 3563 = 3F

60/2 = 30 030/2 = 15 015/2 = 7 17/2 = 3 13/2 = 1 11/2 = 0 1

60/8 = 7 47/8 = 0 7

Page 4: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾

Page 5: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
Page 6: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
Page 7: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
Page 8: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
Page 9: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾

×

Page 10: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
Page 11: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾

(

27×6 + 26×6+1 + 25×6+2 + · · ·)

Page 12: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
Page 13: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
Page 14: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
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010 1

nn

n m

Page 21: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾

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Page 23: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
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Page 31: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
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Page 35: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
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Page 41: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
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Page 43: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
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Page 47: kXN AMi2`M2 2T` b2Mi iBQMpQMw ?H2M - uni … · í S CMFi+?2MQ#2MU7 C`lKH miV¾ ¾Õ¾Í¾Ì¾ ¾ ¾ ¾Ø¾¡¾ ¾ Re3 Ü *QTv`B;?i@w2B+?2M ¾ ¾Ã¾Ï¾Ð¾Ù¾ ¾ ¾ ¾Ø¾¡¾
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