This document discusses converting decimal numbers to binary, octal, and hexadecimal number systems. It provides examples of converting both integers and decimals through long division. The divisions yield a quotient and remainder at each step to derive the place values in the target number system. MSB and LSB designations are used

1. decimal to others
দশমিক থেকক অন্য পদ্ধমিকি রুপান্তর
দশমিক পদ্ধমি
বাইনামি
অক্টাল
হেক্সাডেমিিযাল

2. দশমিক হেডক অনয পদ্ধমিডি রুপান্তি িাডন ভাগ-গুন পদ্ধমি
পূর্ণিংখ্যাডক িাি হবি দ্বািা ভাগ
ভগ্াংশডক িাি হবি দ্বািা গুন

3. (34)10= (? )2, (? )8, (? )16
34/2= 17 0
17/2= 8 1
8/2= 4 0
4/2= 2 0
2/2= 1 0
½= 0 1
পূর্ণ অংশ ভাগডশষ
𝑀𝑆𝐵
𝐿𝑆𝐵
(34)10= (100010)2
 (43)10= (? )2
 (47)10= (? )2

4. (3212)10= (? )2, (? )8, (? )16
(𝟑𝟐𝟏𝟐) 𝟏𝟎= (? ) 𝟐
3212 ÷ 2 = 1606 0
1606 ÷ 2 = 803 0
803 ÷ 2= 401 1
401 ÷ 2= 200 1
200 ÷ 2= 100 0
100 ÷ 2= 50 0
50 ÷ 2= 25 0
25 ÷ 2= 12 1
12 ÷ 2= 6 0
6 ÷ 2= 3 0
3 ÷ 2= 1 1
1 ÷ 2= 𝟎 1
পূর্ণ অংশ
ভাগডশষ
𝑀𝑆𝐵𝑀𝑆𝐵
𝐿𝑆𝐵
(𝟑𝟐𝟏𝟐) 𝟏𝟎= (𝟏𝟏𝟎𝟎𝟏𝟎𝟎𝟎𝟏𝟏𝟎𝟎) 𝟐

5. (𝟗𝟕) 𝟏𝟎= (? ) 𝟐
97/2= 48 1
48/2= 24 0
24/2= 12 0
12/2= 6 0
6/2= 3 0
3/2= 1 1
½= 𝟎 𝟏
𝑀𝑆𝐵
𝐿𝑆𝐵
(𝟗𝟕) 𝟏𝟎= (𝟏𝟏𝟎𝟎𝟎𝟎𝟏) 𝟐

6. (𝟑𝟕) 𝟏𝟎= (? ) 𝟐
(𝟑𝟕) 𝟏𝟎= (𝟏𝟎𝟎𝟏𝟎𝟏) 𝟐

7. (3212)10= (? )8
3212/8= 401 4
401/8= 50 1
50/8= 6 2
6/8= 𝟎 𝟔
decimal to octal
পূর্ণ অংশ ভাগডশষ
(3212)10= (6214)8
 (𝟗𝟖𝟑𝟕) 𝟏𝟎= (? ) 𝟖
 (𝟗𝟖𝟕) 𝟏𝟎= (? ) 𝟖

8. (6475)10= (? )8
(6475)10= (14513)8

9. (576)10= (? )8
576/8= 72 0
72/8= 9 0
9/8= 1 1
1/8= 0 1
(576)10= (1100)8

10. Decimal to Hexadecimal
(5376)10= (? )16
5376/16= 336 0
336/16 21 0
21/16 1 5
1/16 𝟎 𝟏
(5376)10= (1500)16
𝑀𝑆𝐵
𝐿𝑆𝐵

11. (1234)10= (? )16
1234/16 77 2
77/16 4 13 = 𝐷
4/16 0 4
(1234)10= (4𝐷2)16
𝑀𝑆𝐵
𝐿𝑆𝐵

12. (9327)10= (? )16
9327/16 582 15 = 𝐹
582/16= 36 6
36/16= 2 4
2/16= 0 2
(9327)10= (246𝐹)16
𝑀𝑆𝐵
𝐿𝑆𝐵

13. দশমিক অংকশর থেকে
(.175)10= (? )2
.175*2= 0 . 35
.35*2= 0 . 7
.7*2= 1 . 4
.4*2= 0 . 8
……………………………………………………………….
……………………………………………………………..
(.175)10= (.0010 … … )2
পূর্ণ অংশ ভগ্াংশ

14. (. 𝟑𝟓) 𝟏𝟎= (? ) 𝟐
𝑷𝒓𝒂𝒄𝒕𝒊𝒄𝒆

15. (.375)10= (? )2
.375*2= 0 . 75
.75*2= 1 . 5
.5*2= 1 0
(.375)10= (.011)2

16. decimal to octal
(.375)10= (? )8
.375*8= 3 0
(.375)10= (.3)8
পূর্ণ অংশ ভগ্াংশ

17. decimal to octal
(.6779)10= (? )8
.6779*8= 5 . 4232
.4232*8= 3 . 3856
.3856*8= 3 . 0848
.0848*8= 0 . 6784
……………………………………………….
……………………………………………….
(.6779)10= (.5330 … … )8

18. decimal to Hexadecimal
(.6779)10= (? )16
.6779*16= 10 = 𝐴 . 8464
.8464*16= 13 = 𝐷 . 5424
.5424*16= 8 . 6784
.6784 10 = 𝐴 . 8544
…….. …… ….. …… ….
……. ….. …. …. …..
(.6779)10= (. 𝐴𝐷8𝐴 … … . . )16

19. (18.175)10= (? )2
18/2= 9 0
9/2= 4 1
4/2= 2 0
2/2= 1 0
½= 0 1
𝑀𝑆𝐵
𝐿𝑆𝐵
(18)10= (10010)2
.175*2= 0 . 35
.35*2= 0 . 7
.7*2= 1 . 4
.4*2= 0 . 8
….. …. …. ….
…. ….. ….. …..
(.175)10= (.0010 … )2
(18.175)10= (10010.0010 … . )2
𝐿𝑆𝐵
𝑀𝑆𝐵

20. (17.125)10= (? )2
(17.125)10= (10001.001)2

21. (176.125)10= (? )8
176/8= 22 0
22/8= 2 6
2/8= 0 2
(176)10= (260)8
.125*8= 1 0
(.125)10= (.1)8
∴ (176.125)10= (260.1)8

22. 𝑯𝒐𝒎𝒆 𝑾𝒐𝒓𝒌
1. (𝟗𝟖𝟐. 𝟑𝟒𝟓) 𝟏𝟎= (? ) 𝟐, (? ) 𝟖, (? ) 𝟏𝟔
2. (𝟗𝟕𝟖. 𝟏𝟑𝟐𝟓) 𝟏𝟎= (? ) 𝟐, (? ) 𝟖, (? ) 𝟏𝟔
3. (𝟗𝟐. 𝟏𝟐𝟒𝟖) 𝟏𝟎= (? ) 𝟐, (? ) 𝟖, (? ) 𝟏𝟔
4. (𝟖𝟕𝟓. 𝟑𝟗𝟖) 𝟏𝟎= (? ) 𝟐, (? ) 𝟖, (? ) 𝟏𝟔
5. (𝟐𝟑𝟒𝟐. 𝟑𝟒𝟗𝟓) 𝟏𝟎= (? ) 𝟐, (? ) 𝟖, (? ) 𝟏𝟔