Tiêu đề অধ্যায় ৩ সংখ্যা পদ্ধতি ও ডিজিটাল ডিভাইস-03 with solve.pdf ✅

wWwRUvj wWfvBm  ICT Decoder Batch HSC 26------------------------------------------------------------------------------------------1 Rhombus Publications wWwRUvj wWfvBm (Digital Device) Z...Zxq Aa ̈vq Board Questions Analysis m„Rbkxj cÖkœ †evW© mvj XvKv ivRkvnx PÆMÖvg ewikvj h‡kvi wm‡jU Kzwgjø w`bvRcyi gqgbwmsn 2024 2023 2022 eûwbe©vPwb cÖkœ †evW© mvj XvKv ivRkvnx PÆMÖvg ewikvj h‡kvi wm‡jU Kzwgjø w`bvRcyi gqgbwmsn 2024 2023 2022 HSC cixÿv_©x‡`i Rb ̈ evQvBK...Z m„Rbkxj cÖ‡kœvËi cÖkœ1 Bgb evwl©K cixÿvi djvdj we‡kølY Ki‡Z wM‡q †`Lj evsjv, Bs‡iwR I ICT wel‡q †h h_vμ‡g (5C)16, (123)8, (77)10 b¤^i †c‡q‡Q| (K) BDwbfvm©vj †MBU Kx? [Xv. †ev. 24] (L) 17 Gi c‡ii msL ̈vwU 20 e ̈vL ̈v Ki| [Xv. †ev. 24] (M) DÏxc‡K Bg‡bi Bs‡iwR wel‡q cÖvß b¤^i †n·v‡Wwm‡g‡j iƒcvšÍi Ki| [Xv. †ev. 24] (N) DÏxc‡K Bg‡bi wZbwU wel‡q †gvU cÖvß b¤^i evBbvwi‡Z KZ n‡e wbY©q Ki| [Xv. †ev. 24] mgvavb: K †h mKj †MBU Øviv †g.wjK †MBU (AND, OR, NOT) Ges Ab ̈vb ̈ mKj †MBU ev ̄Íevqb Kiv m¤¢e Zv‡`i mve©Rbxb †MBU e‡j| †hgb: NAND, NOR| L A±vj msL ̈v c×wZ Abymv‡i 17 Gi c‡ii msL ̈vwU 20| A±v‡j msL ̈v c×wZi A1⁄4 ̧‡jv n‡jv, 0, 1, 2, 3, 4, 5, 6, 7| G c×wZ‡Z 8, 9 Gi †Kv‡bv Aw ̄ÍZ¡ †bB| d‡j 17 Gi c‡ii msL ̈vwU n‡e 20| cÖwμqvwU wb¤œiƒc: (17)8 = 1  8 1 + 7  8 0 = (15)10 15 +1 16 (16)10 Gi mgZzj ̈ A±vj: 8 16 LSB MSB 8 2  0 0  2 (16)10 = (20)8  178 + 18 = 208 M Bg‡bi Bs‡iwR wel‡q cÖvß b¤^i (123)8| msL ̈vwU A±vj c×wZ‡Z †`qv Av‡Q| msL ̈vwU‡K †n·v‡Wwm‡g‡j iƒcvšÍi Kiv n‡jv: 001 1 2 3 010 011 A±vj evBbvwi  msL ̈vwU evBbvwi c×wZ‡Z = (001 010 011)2 Avevi, 0 0 0 1 0 1 0 0 1 1 5 3 evBbvwi †n·v‡Wwm‡gj  (123)8 = (53)16 myZivs †n·v‡Wwm‡g‡j Bg‡bi cÖvß b¤^i 53| N Bg‡bi evsjv, Bs‡iwR I ICT wel‡q cÖvß b¤^i (5C)16, (123)8, (77)10| b¤^i ̧wj‡K evBbvwi‡Z iƒcvšÍi Kiv n‡jv: 0101 5 C 1100 †n·v‡Wwm‡gj: evBbvwi:  (5C)16 = (01011100)2 [evsjvq cÖvß b¤^i] M n‡Z cvB (123)8 = (1010011)2 [Bs‡iwR‡Z cÖvß b¤^i] AvBwmwU‡Z cÖvß b¤^i evBbvwi‡Z iƒcvšÍi: 2 77 LSB MSB 2 38 – 1 2 19 – 0 2 9 – 1 2 4 – 1 2 2 – 0 2 1 – 0 0 – 1  (77)10 = (1001101)2
2.........................................................................................................................................................................  ICT Chapter-3 Rhombus Publications wZbwU wel‡q †gvU cÖvß b¤^i: evsjv: 1011100 Bs‡iwR: 1010011 ICT: (+) 1001101 = 11111100  Bg‡bi wZbwU wel‡q cÖvß b¤^i evBbvwi‡Z (11 111 100)2 cÖkœ2 Y = (A + B) (A + B – ) (A – A + C) (K) ASCII Kx? [Xv. †ev. 24] (L) we‡qv‡Mi KvR †hv‡Mi gva ̈‡g Kiv m¤¢eÑ e ̈vL ̈v Ki| [Xv. †ev. 24] (M) DÏxc‡K cÖ`Ë jwRK dvskbwUi mZ ̈K mviwY •Zwi Ki|[Xv. †ev. 24] (N) ―Y †K eywjqvb A ̈vj‡Reivi mvnv‡h ̈ mijxKiY Kivi d‡j eZ©bx ev ̄Íevqb mnR n‡q‡QÓÑ we‡kølYc~e©K Dw3wUi mZ ̈Zv hvPvB Ki| [Xv. †ev. 24] mgvavb: K ASCII (American Standard Code for Information Interchange) n‡jv GKwU 7/8 we‡Ui Avjdv wbD‡gwiK †KvW hv Kw¤úDUvi I Input/ output device Gi Z_ ̈ ̄’vbvšÍ‡i e ̈eüZ nq| L evBbvwi msL ̈v c×wZ‡Z 2 Gi cwic~i‡Ki mv‡_ †hv‡Mi gva ̈‡g we‡qv‡Mi KvRwU Kiv m¤¢e| †Kv‡bv msL ̈v‡K 2 Gi cwic~i‡K iƒcvšÍi Kivi A_© n‡jv Zv‡K FYvZ¡K msL ̈vq cwiYZ Kiv| myZivs †Kv‡bv msL ̈vi mv‡_ Aci GKwU msL ̈vi 2 Gi cwic~iK †hvM Kivi A_© n‡jv c~‡e©i msL ̈vwU †_‡K c‡ii msL ̈vwU †_‡K c‡ii msL ̈v we‡qvM Kiv| M DÏxc‡K cÖ`Ë dvskwU n‡jv y = (A + B) (A + B – ) (A – + C) jwRK dvskwUi mZ ̈K mviYx: A B C A – B – A + B A + B – A – + C y = (A + B) (A + B – ) (A – + C) 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 N DÏxc‡Ki y jwRK dvskbwU eywjqvb A ̈vj‡Reivi gva ̈‡g mijxKiY Kiv n‡jv: y = (A + B) (A + B – ) (A – + C) = (A.A + A. B – + A. B + B. B – ) (A – + C) = (A + AB – + A.B + 0) (A – A – + C) [ A.A = A; B. B – = 0] = (A + AB – + AB) (A – + C) = AA – + AC + AA – B – + AB – C + AA – B + ABC [ AA – = 0] = AC + AB – C + ABC = AC (1 + B + B – ) = AC [ 1 + A = A]  mijxK...Z dvskbwUi jwRK eZ©bx: A y = AC C cÖkœ3 P = (36)8 Ges Q = (2F)16 (K) †KvW Kx? [iv. †ev. 24] (L) 11 + 1 = 100 n‡Z cv‡iÑ e ̈vL ̈v Ki| [iv. †ev. 24] (M) P I Q Gi gvb‡K `kwgK msL ̈v c×wZ‡Z cÖKvk Ki| [iv. †ev. 24] (N) (P–Q) MvwYwZK cÖwμqvwU †hv‡Mi gva ̈‡g Kiv hvqÑ MvwYwZKfv‡e we‡kølY Ki| [iv. †ev. 24] mgvavb: K †KvW n‡jv g~jZ evBbvwi msL ̈v hvi Øviv wewfbœ eY©, cÖZxK, AwWI, wfwWI BZ ̈vw` cÖKvk Kiv nq| L evBbvwi msL ̈v c×wZ‡Z 11 + 1 = 100 m¤¢e| evBbvwi msL ̈v c×wZ‡Z ïaygvÎ 1 I 0 we` ̈gvb _vKvi †h‡Kv‡bv msL ̈v‡K ïaygvÎ 1 I 0 Gi gva ̈‡g cÖKvk Kiv nq| evBbvwi‡Z 11 I 1 Gi †hvMdj wb¤œiƒc| evBbvwj: †Wwm‡gj: (11)2  (3)10 +(1)2  +(1)10 (100)2 (4)10 myZivs †Wwm‡g‡j (1)10 = (1)2 , (3)10 = (11)2 I (4)10 = (100)2 nIqvi evBbvwi‡Z 110 + 1 = 100 m¤¢e M DÏxc‡K cÖ`Ë, P = (36)8 Q = (2F)16 P †K `kwgK gv‡b iƒcvšÍi (36)8 = [3  8 1 + 6  8 0 ]10 = [24 + 6]10 = (30)10  (36)8 = (30)10 Q †K `kwgK gv‡b iƒcvšÍi (2F)16 = [2  161 + F  160 ]10 = [2  161 + 15  160 ]10 = (47)10  (2F)16 = (47)10  P I Q †K `kwgK msL ̈v c×wZ‡Z cÖKvk h_vμ‡g (30)10, (47)10 N P-Q MvwYwZK cÖwμqvwU †hv‡Mi gva ̈‡g m¤úbœ Kivi Dcvq n‡jv: evBbvwi msL ̈v c×wZi mvnv‡h ̈, GKwU msL ̈v‡K Aci msL ̈vi 2 Gi cwic~i‡Ki mv‡_ †hvM Kiv| P I Q †K evBbvwi‡Z iƒcvšÍi Kiv n‡jv 011 3 6 110 A±vj: evBbvwi:  (36)6 = (11110)2 = (00011110)2 [8 weU evBbvwi]
wWwRUvj wWfvBm  ICT Decoder Batch HSC 26------------------------------------------------------------------------------------------3 Rhombus Publications Avevi, 0011 2 F 1111 †n·v‡Wwm‡gj: evBbvwi:  (2F)16 = (00101111)2 [8 weU evBbvwi] (2F)16 Gi 1 Gi cwic~iK = 11010000 + 1 (2F)16 Gi 1 Gi cwic~iK = 11010001  (P-Q) = + (36)8 = 11010000 – (2F)16= 11010001 = 1 10100001  wPý weU wPý weU 1 = djvdj FYvZ¡K| djvdj‡K cybivq 2 Gi cwic~iK K‡i cvB| djvdj : 11101111 1 Gi cwic~iK : 00010000 +1 2 Gi cwic~iK : 00010001  P-Q = (1001)2 = (17)10 cÖkœ4 BbcyU AvDUcyU wPÎ-1 X Y K 0 0 1 0 1 0 1 0 1 1 1 1 mZ ̈K mviwY-1 (K) mZ ̈K mviwY Kx? [iv. †ev. 24] (L) A (A + A) = A e ̈vL ̈v Ki| [iv. †ev. 24] (M) K-Gi gvb †jL Ges mij Ki| [iv. †ev. 24] (N) DÏxc‡Ki wPÎ-1 G wb‡`©wkZ †MBUwU w`‡q XOR Gi mgZzj ̈ mvwK©U ev ̄Íevqb Ki| [iv. †ev. 24] mgvavb: K jwRK mvwK©‡Ui Bbcy‡Ui Ici wfwË K‡i AvDUcy‡Ui djvdj †h mviwYi gva ̈‡g cÖKvk, hvPvB I we‡kølY Kiv nq Zv‡K mZ ̈K mviYx e‡j| L A(A + A) = A evgcÿ = A(A + A) = AA [ A + A = A; †g.wjK Dccv` ̈] = A [ A.A = A; †g.wjK Dccv` ̈] = Wvbcÿ M cÖ`Ë mZ ̈K mviwY n‡Z k Gi gvb‡K jwRK dvskb wn‡m‡e cÖKvk K‡i cvB: k = x – y – + xy – + xy = x – y – + x (y – + y) = x – y – + x . 1 [ y – + y = 1] = x – y – + x . (1 + y – ) [ 1 + A = 1] = x – y – + x + xy – = x + (x + x – ) y – = x + y – .1 [ x + x – = 1] = x + y – [ 1.A = A]  k Gi mijxK...Z gvb : x + y – N DÏxc‡K wPÎ-1 G cÖ`wk©Z †MBUwU n‡j NOR †MBU| NOR †MBU GKwU mve©Rbxb †MBU| NOR †MBU w`‡q XOR Gi mgZzj ̈ †MBU ev ̄Íevqb wb¤œiƒc| XOR †MBU Gi jwRK mgxKiY: F = x  y = x – y + xy – mvwKU© WvqvMÖvg: x y F = x  y NOR †MB‡Ui mvnv‡h ̈ ev ̄Íevqb: F = x – y + xy – = x – y ––– ––– + x y –––– ––– = ( ) ——— x –– + y – + ( ) ——— x – + y –– = ( ) —— x + y – + ( ) ——— x – + y = ––––––––––––––– ––––––––– ( —— x + y – ) + ( —— x – + y) mvwKU© WvqvMÖvg: x y x —— x + y – —— x – + y F = –––––––––––– –––––––––––– ( —— x + y – ) + ( —— x – + y)
4 ........................................................................................................................................................................  ICT Chapter-3 Rhombus Publications cÖkœ5 Ab©e jvB‡eawi †_‡K 1wU Kjg I 1wU eB μq Kij| Kjg Gi g~j ̈ (76)8 UvKv Ges eB‡qi g~j ̈ (45)10 UvKv| (K) BDwb‡KvW Kx? [Kz. †ev. 24] (L) 8 + 8 = 10 nqÑ e ̈vL ̈v Ki| [Kz. †ev. 24] (M) DÏxc‡K DwjøwLZ Kjg I eB‡qi †gvU g~j ̈‡K †n·v‡Wwm‡g‡j cÖKvk Ki| [Kz. †ev. 24] (N) DÏxc‡K DwjøwLZ Kjg I eB‡qi g~j ̈ `ywUi cv_©K ̈ †hv‡Mi gva ̈‡g wbY©q Ki| [Kz. †ev. 24] mgvavb: K we‡k¦i †QvU eo mKj fvlv‡K Kw¤úDUv‡ii †KvWfz3 Kivi Rb ̈ †h †KvW e ̈eüZ nq Zv‡K Unicode e‡j| L †n·v‡Wwm‡gj c×wZ‡Z 8 + 8 = 10 nq| A_©vr (8)16 + (8)16 = (10)16 `kwgK c×wZ‡Z (8)10 + (8)10 = (16)10 16 †K †n·v‡Wwm‡g‡j iƒcvšÍi K‡i cvB, 16 16 LSB MSB 16 1 – 0 0 – 1 (16)10 = (16)16  (8)16 + (8)16 = (10)16 M DÏxc‡K cÖ`Ë, Kj‡gi g~j ̈ (76)8 UvKv eB‡qi g~j ̈ (45)10 UvKv Kj‡gi g~j ̈‡K A±vj n‡Z †Wwm‡g‡j iƒcvšÍi (76)8 = (7  8 1 + 6  8 0 )10 = (56 + 6)10 = (62)10 Kjg I eB‡qi †gvU g~j ̈ = [(62)10 + (45)10] = (107)10 UvKv †gvU g~j ̈‡K †n·v‡Wwm‡g‡j iƒcvšÍi: 16 107 LSB MSB 16 6 – 11 (B) 0 – 6  (107)10 = (6B)16  Kjg I eB‡qi †gvU g~j ̈ †n·v‡Wwm‡g‡j = (6B)16 UvKv N Kjg I eB‡qi g~j ̈ `ywUi cv_©K ̈ evBbvwi c×wZ‡Z 2 Gi cwic~iK †hv‡Mi gva ̈‡g wbY©q Kiv n‡jv: Kj‡gi g~j ̈ = (76)8 UvKv 111 7 6 110 A±vj: evBbvwi:  (76)8 = (111110)2 = (00111110)2 [8 weU evBbvwi] eB‡qi g~j ̈ = (45)10 UvKv 2 45 LSB MSB 2 22  1 2 11  0 2 5  1 2 2  1 2 1  0 0  1  (45)10 = (101101)2 = (00101101)2 [8 weU evBbvwi] (45)10 Gi 1 Gi cwic~iK = 11010010 + 1 2 Gi cwic~iK = 11010011 Kjg I eB‡qi g~‡j ̈i cv_©K ̈: Kj‡gi g~j ̈ = 00111110 eB‡qi g~j ̈ (2 Gi cwic~iK) = + 11010011 †hvMdj = 1 00010001  K ̈vwi weU K ̈vwi weU = Ifvi‡d¬v [hv MÖnY‡hvM ̈ bq]  Kjg I eB‡qi g~‡j ̈i cv_©K ̈ (10001)2 cÖkœ6 P Q X F A B wPÎ-1 wPÎ-2 (K) wW‡KvWvi Kx? [Kz. †ev. 24] (L) evBbvwi †hvM Ges eywjqvb †hvM GK bqÑ e ̈vL ̈v Ki| [Kz. †ev. 24] (M) wPÎ-1 Gi F Gi mijxK...Z gvb wbY©q Ki| [Kz. †ev. 24] (N) DÏxc‡Ki wPÎ-2 Gi X Gi gvb‡K ïaygvÎ bi †MB‡Ui mvnv‡h ̈ ev ̄Íevqb m¤¢eÑ wPÎmn we‡kølY Ki| [Kz. †ev. 24] mgvavb: K †h wWwRUvj eZ©bxi mvnv‡h ̈ Computer G e ̈eüZ fvlv‡K gvby‡li †evaMg ̈ fvlvq iƒcvšÍi Kiv nq Zv‡K wW‡KvWvi e‡j| L evBbvwi I eywjqvb †hvM GK bq| evBbvwi msL ̈v c×wZ‡Z ïaygvÎ 1 I 0 we` ̈gvb †h‡Kv‡bv msL ̈v cÖKvk Kivi Rb ̈| G msL ̈v c×wZ‡Z 0, 1, 10, 11, 100 Giƒc msL ̈v we` ̈gvb| wKš‘ eywjqvb A ̈vjReavq ïay 0 Ges 1 we` ̈gvb hv jwRK wg_ ̈v I mZ ̈ cÖKvk K‡i| evBbvwi c×wZ‡Z 1 + 1 = 10, hv cieZ©x msL ̈v| eywjqv‡b 1 + 1 = 1 A_v©r jwRK nvB| myZivs evBbvwi I eywjqvb †hvM GK bq| M wPÎ 1 Gi jwRK mvwK©U: A B F = ———— (A + B –––– + A – ) A – A + B ––––– F = (A + B –––– + A – ) = (A + B ––––– ––– + A –– ) = (A + B) A = A [cwi‡kvlY Dccv` ̈, A (A+B) = A]