Laboratoriya ishi №1 Mavzu: Ikkilik sonlarni kompyuterda ifodalash va ular ustida arifmetik amallarni bajarish. Ishning maqsadi

Misol 7. 27₈ va 146₈ ning ko`paytmasini hisoblang.

Yechish.

Bir sanoq tizimdan ikkinchi sanoq tizimga o`tish
Boshqa sanoq tizimidagi sonlarni o`nlik sanoq tizimiga o`tkazish uchun quyidagi formuladan foydalaniladi:

bunda - berilgan sonning butun qismlari koeffitsientlari; - sanoq tizimining asosi; - sonning kasr qismi.

Misol 8. 101110₂ ikkilik sanoq tizimidagi sonni o`nlik sanoq tizimiga o`tkazing.
Yechish. Yuqoridagi formulaga asosan , . Bu holda,

O’nlik sanoq tizimidagi sonni ixtiyoriy sanoq tizimiga o`girish uchun uni o`zining asosiga bo`lish kerak, toki natija 1 ga teng bo`lgunga qadar.


Misol 9. 37₁₀ sonini ikkilik sanoq tizimida yozing.
Yechish.

Natija: 37₁₀=100101₂

Misol 10. O`nlik sanoq tizimidagi 0,25 sonni ikkilik sanoq tizimida yozing.

Yechish.
Natija: 0,01₂

Ikkilik sanoq sistemasida amallar bajarish
Ikkilik sanoq sistemasida 2 ta raqam: 0 va 1 mavjud. O‘nlik, sakkizlik sanoq sistemasidagi sonlar ikkilik sanoq sistemasida quyidagicha ifodalanadi:

O‘nlik s/s. son	0	1	2	3	4	5	6	7	8	9	10	11
Sakkizlik s/s. son	0	1	2	3	4	5	6	7	10	11	12	13
Ikkilik s/s. son	0	1	10	11	100	101	110	111	1000	1001	1010	1011

Ikkilik sanoq sistemasidagi sonlar ustida turli arifmetik amallar bajarishga oid misollar:

1-misol. 10011+ 11001	2-misol. 1101101,001+1000101,001
Yechish: + 10011 11001 ^----------------- 101100 Javob: 101100	Yechish: +1101101,001 1000101,001 ^------------------------ 10110010,010 Javob: 10110010,010
3-misol. 101010 – 10011 Yechish: – 101010 10011 ----------------- 10111 Javob: 10111	4-misol. 110011,01 – 10111,101 Yechish: - 110011,010 10111,101 ------------------- 11011,101 Javob: 11011,101
5-misol. 110011  101	6- misol. 101,11 11,01
Yechish: 110011 ^ 101 ------------ + 110011 110011 ------------ 11111111 Javob: 11111111	Yechish: 101,11 ^ 11,01 -------------- 10111 + 10111 10111 ------------- 10010,1011 Javob: 10010,1011

7-misol. 1000010010 : 110101	8- misol. 1000000,10011:110,101
Yechish: _1000010’010 110101 110101 1010 _ 110101 110101 0 Javob: 1010	Yechish: _ 100000010’011 11010100 11010100 1001,11 _ 101110 011 11010 100 _ 10011 1110 1101 0100 _ 110 10100 110 10100 0 Javob:1001,11

Mustaqil yechish uchun misollar

1. 
   
   Quyidagi amallarni bajaring
   
   1. 
      
      Ikkilik sanoq tizimida amallarni bajaring
      

1.	1112+1012;	101,112-10,12;	11,12*1,012;
2.	101,112+10,1;	1112-1012;	10,12*1,012;
3.	111012+11012;	100,112-11,12;	1112*1,0012;
4.	111012+11012;	100,112-11,12;	1112*10,12;
5.	1110012+11112;	1000,012-1111,12;	1,012*1,012;
6.	101112+11012;	1001,112-1012;	1,12*1,112;
1.	778+6538;	6278-3678;	358*228.
2.	6778+538;	7228-3678;	458*328.
3.	7658+4538;	6138-4668;	1058*228.
4.	7658+4538;	6138-4668;	1058*228
5.	6078+6538;	6028-3678;	558*768

1. 
   
   Ikkilik sanoq tizimidagi sonlarni o`nlik sanoq tizimida yozing.
   

1.	10111, 112;	7.	101,01012;	13.	10,111112;	19.	111010,1012;
2.	1000,0012;	8.	111010,1012;	14.	111,11100012;	20.	1110,01012;
3.	110,012;	9.	1110,0012;	15.	11100, 01112;	21.	101, 101012;
4.	10,01012	10.	1100,0012;	16.	100011,0012;	22.	1100,110012;
5.	101,1012;	11.	110,001012;	17.	110,0111112;	23.	1101,0011012;

O`nlik sanoq tizimidagi sonlarni ikkilik sanoq tizimida yozing.

1.	12710; 11,2510;	9.	38710; 4,2510;	17.	29710; 421,2510;
2.	23410; 23,510;	10.	17710; 25,12510;	18.	23710; 239,2510;
3.	8610; 34,12510;	11.	34110; 13,0510;	19.	80610; 94,87510;
4.	7510; 10,62510;	12.	10610; 12,62510;	20.	75910; 18,62510;

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