প্রযুক্তি ক্ষেত্রে কম্পিউটারের সাধারণ গাণিতিক ব্যবহার সম্পর্কে ধারণা।
cÖhyw³ †ÿ‡Î Kw¤úDUv‡ii mvaviY MvwYwZK e¨envi m¤ú‡K© aviYv|
msÁv :
mvavišÍ, Kw¤úDUvi †h we‡kl msL¨v e¨envi K‡i Kvh©m¤úbœ K‡i Zv‡K Kw¤úDUvi msL¨v c×wZ e‡j| AZci, Kw¤úDUvi †h c×wZ‡Z wewfbœ msL¨v wj‡L cÖKvk Kiv hvq Ges D³ msL¨vmg~‡ni Dci wewfbœ Acv‡ikb cÖ‡qvM Z_v ‡hvM, we‡qvM, MyY, fvM, kZKivq cÖKvk mn hveZxq wnmve-wbKvk m¤úv`b Kiv hvq Zv‡KB msL¨v c×wZ e‡j|
2 msL¨v Avwe®‹v‡ii BwZnvm :
mf¨Zvi ElvjMœ ‡_‡KB gvbyl cÖ‡hvR‡bi ZvwM‡` wnmve wbKv‡ki Kv‡R Zrci wQj| Z‡e aviYv Kiv nq MYbvi Kv‡R gvbyl me‡P‡q Kv‡Qi I mnRjf¨ nv‡Zi AvOyj‡K cÖ_g e¨envi K‡i| wewfbœ ch©v‡q gvby‡li g‡a¨ Av½y‡ji wMU, bywo cv_i, KvwV, iwk‡Z wMU †`qv, gvwU‡Z ev ‡`qv‡j `vM †K‡U wnmve-wbKvk KiZ|
msL¨v c×wZ :
‡h c×wZ‡Z †Kvb msL¨v wj‡L cÖKvk Kiv Ges D³ msL¨vmg~n‡i Dci wewfbœ Acv‡ikb cÖ‡qvM Z_v †hvM, we‡qvM, MyY, fvM, kZKivq cÖKvk mn hveZxq wnmve-wbKvk m¤úv`b Kiv hvq Zv‡KB nq Zv‡K msL¨v c×wZ e‡j|
4 msL¨v c×wZi cÖKvi‡f` :
MYbv Kivi gva¨gB n‡”Q msL¨v| eZ©gvb we‡k¦ †h msL¨v c×wZ mve©Rbxbfv‡e ¯^xK…Z †mB c×wZ‡K cÖavbZ `yB fv‡M fvM Kiv hvq|
1. bb-cwRkbvj msL¨v c×wZ|
2. cwRkbvj msL¨v c×wZ|
1. bb-cwRkbvj msL¨v c×wZ :
cÖvPxb mf¨Zvq GB msL¨v c×wZi e¨envi wQj eZ©gv‡b Gi cÖPjb †bB ej‡jB P‡j| bb-cwRkbvj msL¨v c×wZ‡Z e¨eüZ A¼My‡jvi †Kvb ¯’vbxq gvb _v‡K bv| †hgb : †ivgvb msL¨v c×wZ GKwU bb-cwRkbvj msL¨v c×wZ|
†ivgvb msL¨v | msL¨vi wbR¯^ gvb |
X | 10 |
XXX | 30 |
wP‡Î : bb-cwRkbvj msL¨v c×wZ
2. cwRkbvj msL¨v c×wZ :
1 | 3 | 5 |
cwRkbvj msL¨v c×wZ‡Z e¨eüZ A¼¸‡jvi ¯’vbxq gvb †_‡K Ges GB cÖwZwU ¯’vwbK gvb wbf©I K‡i A¼wUi †Kv‡bv c×wZ †jLv n‡q‡Q Zvi Ici| Avgv‡`i ‰`bw›`b wnmve-wbKv‡k cwRkbvj msL¨v c×wZ e¨envi Kiv nq| G c×wZ‡Z †Kvb msL¨vi gvb Rvb‡Z †mB msL¨vi wbR¯^ gvb, msL¨vwUi wfwË I msL¨vwU‡Z e¨eüZ A¼¸‡jvi Ae¯’vb Rvb‡Z nq| †hgb :
GLv‡b,135=1×100+3×10+5×1
=1×102+3×101+5×100
cwRkbvj msL¨v c×wZ‡Z cÖwZwU msL¨v‡K i¨vwW· (Radix) c‡q›U (,) w`‡q c~Y©vsk (Integer) I fMœvsk (Fraction) G `yÕ As‡k fvM Kiv nq| ‡hgb-135.265| GLv‡b 135 c~Y© msL¨v, (.) i¨vwW· c‡q›U I .265 fMœvsk|
=1×102+3×101+5×100
cwRkbvj msL¨v c×wZ‡Z cÖwZwU msL¨v‡K i¨vwW· (Radix) c‡q›U (,) w`‡q c~Y©vsk (Integer) I fMœvsk (Fraction) G `yÕ As‡k fvM Kiv nq| ‡hgb-135.265| GLv‡b 135 c~Y© msL¨v, (.) i¨vwW· c‡q›U I .265 fMœvsk|
3. cwRkbvj msL¨v c×wZi cÖKvi‡f` :
wewfbœ mgq wewfbœ msL¨v c×wZi cÖPjb _vK‡jI AvaywbK hy‡M wewfbœ ai‡bi B‡jKUªwbK š¿cvwZ wb‡q KvR Ki‡Z nq hvi Rb¨ Awfbe msL¨v c×wZi cÖPjb n‡q‡Q| cwRkbvj msL¨v c×wZ Pvi ai‡bi|h_v-
1) evBbvwi ev wØwgK msL¨v c×wZ|
2) A±vj ev AówgK msL¨v c×wZ|
3) †Wwm‡gj ev `kwgK msL¨v c×wZ Ges
4) ‡n·v‡Wwm‡gj ev †lvo`k msL¨v c×wZ|
1. evBbvwi msL¨v c×wZ (Binary Number System) :
1) evBbvwi ev wØwgK msL¨v c×wZ|
2) A±vj ev AówgK msL¨v c×wZ|
3) †Wwm‡gj ev `kwgK msL¨v c×wZ Ges
4) ‡n·v‡Wwm‡gj ev †lvo`k msL¨v c×wZ|
1. evBbvwi msL¨v c×wZ (Binary Number System) :
‡h msL¨v c×wZ‡Z msL¨v MYbv Kivi Rb¨ gvÎ 2 (`yB) wU A¼ ev wPý e¨eüZ nq Zv‡K evBbvix msL¨v c×wZ e‡j| evB A_© 2 (`yB)| evBbvix msL¨v c×wZ‡Z e¨eüZ cÖwZK ev A¼ (digit) `ywU n‡jv (2) Ges (1)| ZvB evBbvix msL¨v c×wZi wfwË n‡jv 2| evBbvix msL¨v c×wZ cÖwZwU wPý‡K Bit (Binary digit Gi mswÿß iƒc) e‡j, GwU mijZg msL¨v c×wZ| †hgb – (101010)2 GKwU evBbvix msL¨v|
Date: 03-03-2019 Part: 02
Day : 02 Job :01.1
K. Kw¤úDUv‡i evBbvwi msL¨v c×wZ e¨envi :
Kw¤úDUvi B‡jKwUªK¨vj wmMb¨v‡ji mvnv‡h¨ KvR K‡i| B‡jKwUªK¨vj wmMb¨v‡ji mvnv‡h¨ `kwgK msL¨vq `kwU wfbœ wfbœ Ae¯’v (0,1,2,3,4,5,6,7,8,9) cÖKvk Kiv Lye KwVb| wKšÍ B‡jKwUªK¨vj wmMb¨v‡ji mvnv‡h¨ evBbvix msL¨vq `ywU Ae¯’v (0,1) Lye mn‡RB cÖKvk Kiv hvq|
L. evBbvwi msL¨v c×wZi ¸iæZ¡ :
evBbvwi msL¨v c×wZi wfwË n‡jv 2| evBbvwi msL¨v c×wZ‡Z gvÎ GB `ywU 0 Ges 1 wPý e¨envi Kiv nq e‡j G‡K evBbvwi msL¨v c×wZ ejv nq| Kw¤úDUv‡i e¨eüZ mvwK©U¸‡jv we`y¨‡Zi High ‡fv‡ëR I Low ‡fv‡ë‡Ri wfwˇZ KvR K‡i | High ‡fv‡ëR‡K weU-1 Ges Low ‡fv‡ëR‡K weU-0 w`‡q wb‡`©k Kiv nq| Avevi, GKwU myBP Ad (OFF) A_ev Ab (ON) n‡Z cv‡i|
2. A±vj msL¨v c×wZ :
‡h msL¨v c×wZ‡Z msL¨v MYbv Kivi Rb¨ 8 (AvU) wU A¼ ev cÖZxK e¨envi Kiv nq Zv‡K A±vj msL¨v c×wZ e‡j| A± A_© 8 (AvU)| A±j msL¨v c×wZ‡Z e¨eüZ cÖwZK ev A¼ (wWwRU) ¸‡jv 0,1,2,3,4,5,6 I 7| ZvB A±vj msL¨v c×wZi wfwË n‡jv 8| †hgb-(127)8 GKwU A±j msL¨v|
3. ‡Wwm‡gj msL¨v c×wZ :
‡h msL¨v c×wZ‡Z msL¨v MYbv Kivi Rb¨ 10 (`k) wU A¼ ev cÖZxK e¨envi Kiv nq Zv‡K ‡Wwm‡gj msL¨v c×wZ e‡j| †Wwm A_© (10) `k| ‡Wwm‡gj msL¨v c×wZ‡Z e¨eüZ cÖwZK ev A¼ (wWwRU) ¸‡jv 0,1,2,3,4,5,6,7,8 Ges 9| ZvB A±vj msL¨v c×wZi wfwË n‡jv 10| †hgb- (99)10 GKwU †Wwm‡gj msL¨v|
4. ‡n·v‡Wwm‡gj msL¨v c×wZ :
‡h msL¨v c×wZ‡Z 16 (‡lvj) wU A¼ ev cÖZxK e¨envi Kiv nq Zv‡K †n·v‡Wwm‡gj msL¨v c×wZ e‡j| †n·v‡Wwm‡gj k‡ãi †n· (Hex) A_© 6 Ges AciwU †Wwm‡gj (Decimal) A_© 10, `y‡Uv wg‡j n‡jv 16| †n·v‡Wwm‡gj msL¨v c×wZ‡Z e¨eüZ cÖwZK ev A¼ (wWwRU) ¸‡jv 0,1,2,3,4,5,6,7,8,9; A, B, C, D, E Ges F ZvB ‡n·v‡Wwm‡gj msL¨v c×wZi wfwË n‡jv 16| †hgb- (6D)16 GKwU †n·v‡Wwm‡gj msL¨v|
v msL¨v c×wZi wfwË ev †eR :
‡Kvb msL¨v c×wZi ‡eR ev wfwË ej‡Z H c×wZ‡Z e¨eüZ †gvU A¼mg~‡ni msL¨v eySvq| A_©vr GKwU msL¨v c×wZ‡Z hZ¸‡jv A¼ ev wPý e¨eüZ Mq Zv‡`i msL¨v‡K H msL¨v c×wZi wfwË ev †eR e‡j|
wb‡P wewfbœ cÖKvi msL¨v c×wZi bvg, cÖwZK, †eR I D`vniY †`Lv‡bv n‡jv :
msL¨v c×wZ | ‡eR ev wfwË | cÖwZK ev wPý | D`vniY | |
evBbvwi | 2 | 0,1 | (101010)2 | |
A±vj | 8 | 0,1,2,3,4,5,6,7 | (127)8 | |
‡Wwm‡gj | 10 | 0,1,2,3,4,5,6,7,8,9 | (99)10 | |
‡n·v‡Wwm‡gj | 16 | 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F | (6D)16 | |
v evBbvwi, A±vj, ‡Wwm‡gj, ‡n·v‡Wwm‡gj msL¨v My‡jvi Zzjbvg~jK QK :
‡Wwm‡gj | A±vj | evBbvwi | ‡n·v‡Wwm‡gj |
0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 |
2 | 10 | 2 | 2 |
3 | 11 | 3 | 3 |
4 | 100 | 4 | 4 |
5 | 101 | 5 | 5 |
10 | 1010 | 12 | A |
cwi‡k‡l ejv hvq, Kw¤úDUvi wewfbœ cª‡qR‡b wewfbœ ai‡bi msL¨v c×wZi D™¢e I cªPjb n‡q‡Q| Z‡e †h mKj msL¨vmg~n eZ©gvb we‡k¦ me †P‡q ‡ewk RbwcÖq Dc‡i D‡jøwLZ msL¨v c×wZ ¸‡jv ewY©Z n‡q‡Q|
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