Namangan davlat universiteti amaliy matematika kafedrasi
Amaliy mashg`ulot mavzu rejasi
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Amaliy mashg amaliy matematika 1 kurs
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Amaliy mashg`ulot mavzu rejasi:
Sanoq sistema haqida tushuncha. Sanoq sistema ustida amallar. Quyidagi 10 li sanoq sistemasidagi sonlarni 2 li, 8 li va 16 li sanoq sistemasidagi o’tkazing . (а,в,д) a) 26710 →X2 b) 26710 →Y8 c) 26710 →X16 d) 267,6810 →X2 e) 267,6810 →Y8 f) 267,6810 →X16 Topshiriqni bajarish: 267| 8 b) 264| 33| 8 3 32| 4 1 Demak, 26710=4138 267| 2 a) 266| 133| 2 1 132| 66| 2 1 66| 33| 2 0 32| 16| 2 1 16| 8| 2 0 8| 4| 2 0 4| 2| 2 0 2| 1 0 Demak, 26710=1000010112 267| 16 c) 256| 16| 16 11 16| 1 0 Demak, 26710=10B16 Berilgan misoldagi sonlarni butun qismi yuqorida aniqlangan. Shuning uchun ularni kasr qismi ustida amallarni bajaramiz. d) x 0,68 x 0,36 x 0,72 … Demak, 267,6810=100001011,1012 2 2 2 1,36 0,72 1,44 e) x 0,68 x 0,44 x 0,52 ... Demak, 267,6810=413,5348 8 8 8 5,44 3,52 4,16 f) x 0,68 x 0,88 x 0,08 … Demak, 267,6810= 10B,AE116 16 16 16 10,88 14,08 1,28 2-Topshiriq.Quyidagi sonlarni 10 li sanoq sistemasiga o’tkazing. (а, в, д, е) a) 100001011,1012 →X10 100001010,1012=1*28+0*27+0*26+0*25+0*24+1*23+0*22+1*21+1*20+1*2-1+0*2-2+1*2-3= 256+8+2+1+0,5+0,125=267,62510 b) 413,5348→Y10 413,5348=4*82+1*81+3*80+5*8-1+3*8-2+4*8-3=256+8+3+0,625+0,1725+0,0156≈267,6810 c) 10B,AE116→Z10 10B,AE116=1*162+0*161+11*160+10*16-1+14*16-2+1*16-3=256+11+0,625+0,054+0,01 ≈267,6810 3-Topshiriq. Quyidagi yig’indini hisoblang. (а, в, г, д). Olingan natijalarni tekshiring. a) 100000001002 + 1110000102 = 101110001102 + 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 b) 232,28 + 427,548 = 662,748 + 232,2 427,54 661,74 Tekshirish: 232,28=2*82+3*81+2*80+2*8-1=128+24+2+0,25=154,2510 427,548=4*82+2*81+7*80+5*8-1+4*8-2=256+16+7+0,625+0,0625=279,687510 661,748=6*82+6*81+1*80+7*8-1+4*8-2=384+48+1+0,875+0,0625=433,937510 154,2510+279,687510=433,937510 c) 3B3,616 + 38B,416 = 73E,A16 + 3B3,6 38B,4 73E,A Tekshirish: 3B3,616=3*162+11*161+3*160+6*16-1=768+176+3+0,375=947,37510 38B,416=3*162+8*161+11*160+4*16-1=768+128+11+0,25=907,2510 73E,A16=7*162+3*161+14*160+10*16-1=1792+48+14+0,625=1854,62510 947,37510+907,2510=1854,62510 4-Topshiriq. Quyidagi ayirmani hisoblang. (а, в, г, д). Olingan natijalarni tekshiring. а) 1100000011,0112 – 101010111,12=110101011,1112 - 1 1 0 0 0 0 0 0 1 1,0 1 1 1 0 1 0 1 0 1 1 1,1 0 0 1 1 0 1 0 1 0 1 1,1 1 1 Tekshrish: 1100000011,0112=1*29+1*28+0*27+0*26+0*25+0*24+0*23+0*22+1*21+1*20+0*2-1+1*2-2+1*2-3= =512+256+2+1+0,25+0,0625=771,312510 101010111,12=1*28+0*27+1*26+0*25+1*24+0*23+1*22+1*21+1*20+1*2-1= 256+64+16+4+2+1+0,5=343,510 110101011,1112=1*28+1*27+0*26+1*25+0*24+1*23+0*22+1*21+1*20+1*2-1+1*2-2+1*2-3= 256+128+32+8+2+1+0,5+0,25+0,0625=427,812510 771,312510 -343,510=427,812510 б) 1510,28 – 1230,548= 257,448 - 1510,20 1230,54 257,44 Tekshrish: 1510,28 = 1*83+5*82+1*81+0*80+2*8-1 =512+320+8+0,25=840,2510 1230,548 = 1*83+2*82+3*81+0*80+5*8-1+4*8-2=512+128+24+0,625+0,0625=664,687510 257,448 = 2*82+5*81+7*80+4*8-1+4*8-2=128+40+7+0,5+0,0625=175,562510 840,2510 - 664,687510 = 175,562510 в) 27D,D816 -191,216 = EC,B816 - 27D,D8 191, 20 EC,B8 Tekshrish: 27D,D816 = 2*162+7*161+13*160+13*16-1+8*16-2 =512+112+13+0,8125+0,03125=637,8437510 191, 216 = 1*162+9*161+1*160+2*16-1=256+144+1+0,125= 401,12510 EC,B816 = 14*161+12*160+11*16-1+8*16-2 = 224+12+0,6875+0,03125=236,7187510 637,8437510 - 401,12510 = 236,7187510 5-Topshiriq. Quyidagi ko’paytmani hisoblang.(а, б, в) а) 1001112 ∙ 10001112 = 1010110100012 x 100111 1000111 100111 + 100111 100111 100111______ 101011010001 Tekshirish: 1001112 = 1*25+0*24+0*23+1*22+1*21+1*20 = 32+4+2+1 = 3910 10001112 =1*26+0*25+0*24+0*23+1*22+1*21+1*20 =64+4+2+1 = 7110 1010110100012 = 1*211+0*210+1*29+0*28+1*27+1*26+0*25+1*24+0*23+ 0*22+0*21+1*20 = =2048+512+128+64+16+1=276910 3910 ∙ 7110 = 276910 x 0,805 x 0,44 x 0,52 8 8 8 6,440 3,52 4,16 606| 8 600| 75| 8 6 72| 9| 8 3 8| 1 1 б) 17,648 ∙ 46,38 = 1136,6348 17,648 = 1*81+7*80+6*8-1+4*8-2 = 8+7+0,75+0,0625=15,812510 46,38 = 4*81+6*80+3*8-1= 32+6+0,375=38,37510 15,812510 ∙ 38,37510 = 606,80510 с) 21,A16 ∙ 10,D16 =24B,DCE16 21,A16=2*161+1*160+10*16-1=32+1+0,625=33,062510 10,D16=1*161+0*160+13*16-1=16+0,8125=16,812510 33,062510 ∙ 16,812510 =555,86310 555|16 544| 34|16 11 32| 2 4 X 0,863 X 0,808 X 0,928 16 16 16 13,808 12,928 14,848 Sanoq sistema jadvali
Bir sanoq sanoq sistemadan ikkinchisiga o`tkazish. 22 = 4, 23 = 8, 24 = 16, 32 = 9, 42 = 16. Demak, 2 ↔ 4, 2 ↔ 8, 2 ↔ 16, 3 ↔ 9, 4 ↔ 16 sanoq sistemalarga o`tkazish mumkin. Misol-6. 1100111101112 → X4. Buning uchun o`ngdan chapga qarab 2 xonadan ajratib chiqamiz. 11’00’11’11’01’11. Endi jadvaldan foydalanib 2 lik jadval ustunidan 4 lik jadval ustuniga mos holda qiymatlarni qo`yamiz: 3033134 Misol-7. 2607504518 → X2. Buning uchun chapdan o`ngga qarab har bir raqamni 3 xona shaklida ifodalab olamiz. agar 3 xonadan kam bo`lsa, raqam oldiga 0 lar bilan to`ldirib olinadi. Jadvaldan foydalanib quyidagicha: 260750451 → 010 110 000 111 101 000 100 101 001 bo`ladi. Demak, 2607504518 → 101100001111010001001010012 . Misol-8. 26AFDC0E116 → X8. Buning uchun quyidagi qonuniyatt asosida amalga oshiramiz: Z16 → Y2 → X8. Demak, dastlab 2 likka keyin 8 lik sanoq sistemaga o`tkazish mumkin ekan. 26AFDC0E1 → 0010 0110 1010 1111 1101 1100 0000 1110 0001. 1001101010111111011100000011100001→ 001 001 101 010 111 111 011 100 000 011 100 001→1 1 5 2 7 7 3 4 0 3 4 18 Javob: 26AFDC0E116 → 1152773403418. 6-Topshiriqlar. Amallar bajaring. a) 1214128 → X2. b) FAA141C8 → X2 . c) 3212024 → X16. d) 72320128 → X4. Download 0.52 Mb. Do'stlaringiz bilan baham: 
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