Full Description of Digital Numbering System!??

Trickworld

31 Oct, 2018

Full Description of Digital Numbering System

gvbe mf¨Zvi m~PbvjMoe n‡Z ïiæ K‡i GwUi μgweKv‡ki mv‡_ mv‡_ gvbyl MYbv Z_v wnmve-wbKv‡mi

cÖ‡qvRbxqZv Abyfe Ki‡Z _v‡K| cÖvPxbKv‡j MYbvi Rb¨ nv‡Zi Av½yj, bywo cv_i, wSbyK, KvwV,

iwki wMU, †`qv‡j `vM KvUv BZ¨vw` e¨envi Ki‡Zv| mg‡qi weeZ©‡b DboewZi avivevwnKZvq MYbvi

†ÿ‡Î hy³ n‡jv wewfboe cÖZxK I wP‡ýi e¨envi| eZ©gv‡b gvbyl MYbvi Rb¨ `kwgK msL¨v c×wZ

e¨envi K‡i| Kw¤úDUvi KvR K‡i evBbvwi msL¨v c×wZ‡Z| GQvovI Kw¤úDUvi KvR K‡i AKU¨vj, †n·v‡Wwm‡gj I wewfboe †Kv‡Wi gva¨‡g| Kw¤úDUv‡ii hveZxq MvwYwZK I hyw³g~jK KvR eySvi Rb¨

eywjqvb A¨vj‡Reiv, jwRK †MBU, wW-giM¨v‡bi Dccv`¨, Gb‡KvWvi, wW‡KvWvi, A¨vWvi, †iwR÷vi I

KvD›Uvi BZ¨vw` m¤ú‡K© Rvbv cÖ‡qvRb|

History of the Numbering System:

Digital Number

gvbe mf¨Zvi m~PbvjMoe n‡Z ïiæ K‡i GwUi μgweKv‡ki mv‡_ mv‡_ gvbyl MYbv Z_v wnmve-wbKv‡mi

cÖ‡qvRbxqZv Abyfe Ki‡Z _v‡K| cÖvPxbKv‡j MYbvi Rb¨ bvbv iKg DcKiY e¨envi Kiv n‡Zv|

h_v: nv‡Zi Av½yj, bywo cv_i, wSbyK, KvwV, iwki wMU, †`qv‡j `vM KvUv BZ¨vw`| mg‡qi weeZ©‡b

DboewZi avivevwnKZvq MYbvi †ÿ‡Î hy³ n‡jv wewfboe cÖZxK I wP‡ýi e¨envi| wLª÷c~e© 3400 mv‡j

nvqv‡ivwMøwd· (Hieroglyphics) wPý ev msL¨v c×wZi gva¨‡g me©cÖg MYbvi Kv‡R wjwLZ msL¨v ev

wP‡ýi cÖPjb ïiæ nq| Gici ch©vqμ‡g †gqvb (Mayan) I †ivgvb (Roman) msL¨v c×wZ

e¨env‡ii cÖPjb ïiæ nq| cieZ©x‡Z fviZel© I Avi‡e `kwgK msL¨v c×wZi cÖPjb ïiæ nq- hv

eZ©gv‡b evsjv‡`kmn mviv we‡k¦i wewfboe †`‡k wnmve-wbKv‡mi Rb¨ e¨vcK RbwcÖqZv AR©b K‡i Ges

AvRI eûwea MvwYwZK Kv‡R eûj e¨eüZ n‡‛Q|

Type of Number System:

Classification of Number System.

†Kv‡bv msL¨v cÖKvk Kivi c×wZ‡K e‡j msL¨v c×wZ| Ab¨ K_vq, †h c×wZi gva¨‡g msL¨v cÖKvk I

MYbv Kiv nq Zv‡K msL¨v c×wZ e‡j| msL¨v cÖKvk Kivi wewfboe cÖZxKB n‡‛Q A¼| †hgb: 125

msL¨vwU 1, 2, I 5 G wZbwU A¼ Øviv MwVZ|

mf¨Zvi ïiæ †_‡K AvR ch©šÍ †hme msL¨v c×wZi cÖPjb n‡q‡Q Zv‡`i‡K cÖavbZt `ywU fv‡M fvM

Kiv hvq| h_v:

1.bb-cwRkbvj(Non-Positional) msL¨v c×wZ|

1.cwRkbvj (Positional)msL¨v c×wZ|

(Non-Positional) msL¨v c×wZ:

GKwU cÖvPxbZg c×wZ n‡‛Q bb-cwRkbvj msL¨v c×wZ| eZ©gv‡b G c×wZi cÖ‡qvM LyeB Kg|

†h msL¨v c×wZ‡Z †Kv‡bv msL¨vq e¨eüZ wPý ev A¼mg~n †Kv‡bv ¯’vbxq gvb ev Ae¯’v‡bi Dci

wbf©i K‡i bv, Zv‡K bb-cwRkbvj msL¨v c×wZ e‡j| msL¨vi g‡a¨ e¨eüZ A¼¸‡jv †Kvb

Ae¯’v‡b Av‡Q Zvi †Kv‡bv cÖfve †bB| msL¨vq e¨eüZ A¼ †hLv‡bB _vKzK bv †Kb G‡`i wbR¯^

gvb ØvivB msL¨vwUi gvb wba©viY Kiv nq| †hgb- cÖvPxb nvqv‡ivwMøwd· msL¨v c×wZ|

(Positional) msL¨v c×wZ:

eZ©gv‡b me‡P‡q ¸iæZ¡c~Y© I eûj cÖPwjZ msL¨v c×wZ n‡‛Q cwRkbvj msL¨v c×wZ| †h msL¨v c×wZ

cÖKvk Kivi Rb¨ msL¨v c×wZ‡Z e¨eüZ †g․wjK wPý, †eR ev wfwË Ges Gi Ae¯’vb ev ¯’vbxqgvb _vK‡Z

nq Zv‡K cwRkbvj msL¨v c×wZ e‡j| †hgb evBbvwi msL¨v c×wZ‡Z 0 I 1 G `ywU †g․wjK wPý e¨eüZ nq

Ges †eR n‡‛Q 2| wWwR‡Ui Ae¯’v‡bi Dci msL¨vi gvb wbf©i K‡i| GRb¨ evBbvwi msL¨v c×wZ‡K

cwRkbvj msL¨v c×wZ e‡j| cwRkbvj msL¨v c×wZ‡Z †Kv‡bv GKwU msL¨vi gvb †ei Kivi Rb¨ wZbwU

Dcv`v‡bi cÖ‡qvRb nq| h_v:

1. msL¨vwU‡Z e¨eüZ A¼¸‡jvi wbR¯^ gvb,

2. msL¨v c×wZi †eR (Base) ev wfwË,

3. msL¨vwU‡Z e¨eüZ A¼¸‡jvi Ae¯’vb ev ¯’vbxq gvb|

cwRkbvj msL¨v c×wZ‡Z cÖwZwU msL¨v‡K i¨vwW· (Radix) c‡q›U (.) w`‡q c~Y©vsk (Integer) I

fMoevsk (Fraction) G `yAs‡k fvM Kiv nq|

msL¨v c×wZi (Base):

†Kv‡bv msL¨v c×wZi †eR ev wfwË n‡‛Q H msL¨v c×wZ‡Z e¨eüZ †g․wjK wPýmg~‡ni †gvU msL¨v|

†hgb- evBbvwii †eR 2| KviY G c×wZ‡Z †gvU 2wU †g․jK wPý Av‡Q| †hgb- 0 I 1|

Ab¨ K_vq, †Kv‡bv GKwU msL¨v c×wZ‡Z e¨eüZ †g․wjK cÖZxK ev A‡¼i †gvU msL¨v‡K D³ msL¨v

c×wZi †eR (Base) ev wfwË ejv nq| †eR Øviv †Kv‡bv GKwU msL¨v, †Kvb msL¨v c×wZi

msL¨v Zv wbiƒcY Kiv nq| †hgb-`kwgK msL¨v c×wZi †eR 10, evBbvwi msL¨v c×wZi

†eR 2, AKU¨vj I †n·v‡Wwmgvj msL¨v c×wZi †eR h_vμ‡g 8 I 16|

কজের ধরন ও হিসাব নিকাসের ভিত্তিতে বিভিন্ন প্রকার সংখ্যা পদ্বতি প্রচলন ও ব্যবহার রয়েছে ।

যথা:

1. `kwgK msL¨v c×wZ (Decimal Number System)

2. evBbvwi msL¨v c×wZ (Binary Number System)

3. AKU¨vj msL¨v c×wZ (Octal Number System)

4. †n·v‡Wwmgvj msL¨v c×wZ (Hexadecimal Number System)

দশমিক সংখ্যা পদ্বতি (Decimal Number System) :

mvaviY wnmve-wbKv‡mi Rb¨ `kwgK msL¨v c×wZ e¨envi Kiv nq| †h msL¨v c×wZ‡Z 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, G `kwU A¼ ev wPý e¨envi Kiv nq Zv‡K `kwgK msL¨v c×wZ e‡j|

10| উদাহরণ: (125)10

Decimal Number

বাইনারি সংখ্যা পদ্ধতি (Binary Number System) :

evBbvwi msL¨v c×wZ GKwU mijZg msL¨v c×wZ| Kw¤úDUv‡ii Af¨š ÍixY KvR সম্পাদন nq evBbvwimsL¨v c×wZ‡Z| 0 I 1 G `ywU A¼‡K Binary digit ev ms‡ÿ‡c Bit ejv nq| †h msL¨v c×wZ‡Z 0 I 1

G `ywU A¼ e¨envi Kiv nq Zv‡K evBbvwi msL¨v c×wZ e‡j| evBbvwi msL¨v c×wZ‡Z †h‡nZz 2wU A¼

e¨envi Kiv nq| myZivs GwUi †eR ev wfwË 2|

Binary Number

অকট্যাল সংখ্যা পদ্ধতি (Octal Number System):

evBbvwi msL¨v 2 Gi wfwË‡Z MwVZ e‡j GwU †ewk `xN©| G‡K mnR I †QvU Kivi Rb¨ Av‡iv `ywU msL¨v c×wZi D™¢e nq| Gi GKwU AKU¨vj msL¨v c×wZ| AvaywbK wWwRUvj Kw¤úDUv‡I AKU¨vj msL¨v c×wZ e¨eüZ n‡‛Q| †h msL¨v c×wZ 0, 1, 2, 3, 4, 5, 6, 7 G AvUwU A¼ ev wPý wb‡q MwVZ Zv‡K

AKU¨vj msL¨v c×wZ e‡j| G 8 wU †g․wjK A¼ ev wPý wb‡q hveZxq MvwYwZK Kg©KvÐ m¤úv`b Kiv nq e‡j Gi †eR ev wfwË n‡jv 8| G c×wZ‡Z 8 Ges 9 Gi †Kv‡bv Aw¯ÍZ¡ †bB| AKU¨vj msL¨v c×wZ‡Z GKwU AKU¨vj msL¨v wZbwU Binary digit †K Represent K‡i|

হেক্সাডেসিমাল সংখ্যা পদ্ধতি (Hexadecimal Number System)

†h msL¨v c×wZ‡Z 16wU wPý ev A¼ Av‡Q, †mB msL¨v c×wZ‡K †n·v‡Wwm‡gj msL¨v c×wZ e‡j|

†n·v‡Wwmgvj msL¨v c×wZi †g․wjK A¼ ev cÖZxK †gvU 16wU| h_v: 0, 1, 3, 4, 5, 6, 7, 8, 9,Ges, A, B, C, D, E, F | G 16 wU †g․wjK cÖZxK ev A¼ e¨envi K‡i mKj cÖKvi MvwYwZK wnmve- wbKvm m¤úv`b Kiv

nq| †h‡nZz GLv‡b 16 wU A¼ ev cÖZxK e¨envi Kiv nq| ZvB †n·v‡Wwmgvj msL¨v c×wZi †eR ev wfwË n‡jv 16| mycvi Kw¤úDUvi, †gBb‡d«g Kw¤úDUv‡I †n·v‡Wwmgvj msL¨v c×wZ e¨eüZ n‡‛Q| cv‡ki mviwY‡Z `kwgK msL¨vi mgZzj¨ †n·v‡Wwmgvj msL¨vi gvb †`Lv‡bv n‡jv :