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CSE Assignment
Name: Md. Raihan
Dept: CSE
Course: cse105
ID: 2012-2-60-040
sce: 4
(111000110010)₂ conversion                    base2 to base8 conversion
                                              Equivalent value list
Binary to octal→
                                                     binary    Octal
base2(binary)= 111000110010
base8(octal)= 7062 oct
                                                     000       0
So, (111000110010)₂=(7062)₈
                                                     001       1
binary to decimal→
Base8(octal)= 7062                                   010       2
            = 7*8³+0*8²+6*8¹+2*8°
                                                     011       3
            = 3634 dec
So, (111000110010)₂=(3634)₁₀
                                                     100       4
binary to hexadecimal →
                                                     101       5
                remainder
3634/16= 227       2 in hexadecimal form             110       6
227/16 = 14         3 in hexademal form
14/16 = 0          14=E in hexadecimal form          111       7

So,(111000110010)₂=(E32)₁₆
(70642)₈ conversion
Octal to decimal→
Oct= 76042 = 7*8´+6*8³+0*8²+4*8¹+2*8° = 31778 dec
So, (76042)₈= (31778)₁₀
                         Decimal
                                   Operation   Quotient Remainder   Binary Result
                         Number
octal to binary→         31778     ÷2=         15889     0          0
                         15889     ÷2=         7944      1          10
                         7944      ÷2=         3972      0          010
                         3972      ÷2=         1986      0          0010
                         1986      ÷2=         993       0          00010
                         993       ÷2=         496       1          100010
                         496       ÷2=         248       0          0100010
                         248       ÷2=         124       0          00100010
                         124       ÷2=         62        0          000100010
                         62        ÷2=         31        0          0000100010
                         31        ÷2=         15        1          10000100010
                         15        ÷2=         7         1          110000100010
                         7         ÷2=         3         1          1110000100010
                         3         ÷2=         1         1          11110000100010
                         1         ÷2=         0         1          111110000100010
Octal to hexadecimal→

(76042)₈= (31778)₁₀

Decimal    operation    quotient remainder
number
31778      ÷16 =        1986     2
1986       ÷16=         124      2
124        ÷16 =        7        12=C
7          ÷16=         0        7
0          Done.


So,
  (76042)₈=(7C22)₁₆
(786)₁₀ conversion

Decimal to binary→
Decimal      operation   quotient   remainder   Binary result
number
786          ÷2=         393        0           0
393          ÷2=         196        1           10
196          ÷2=         98         0           010
98           ÷2=         49         0           0010
49           ÷2=         24         1           10010
24           ÷2=         12         0           010010
12           ÷2=         6          0           0010010
6            ÷2=         3          0           00010010
3            ÷2=         1          1           100010010
1            ÷2=         0          1           1100010010

 So, (786)₁₀=(1100010010)₂
Decimal to octal→
  Decimal                                             Octal
               Operation       Quotient   Remainder
  Number                                              Result
  786        ÷8=                98           2        2
  98         ÷8=                12           2        22
  12         ÷8=                 1           4        422
  1          ÷8=                 0           1        1422
  0          done.

So, (786)₁₀ = (1422)₈
Decimal to hexadecimal→
  Decimal                                             Hexadecimal
               Operation       Quotient   Remainder
  Number                                              Result
  786         ÷ 16 =             49          2        2
  49          ÷ 16 =              3          1        12
  3           ÷ 16 =              0          3        312=3C
  0           done.
So, (786)₁₀= (312)₁₆ =(3C)₁₆
FA09 conversion
                                              Hexa-decimal value list:
Hexa-dec to decimal→
FA09 hexadecimal:                                 Hexa
                                                              0    1   2    3    4    5    6    7
                                                  decimal:
= ((F)*163) + ((A)*162) + (0*161) + (9*160)
= (15*163) + (10*162) + (0* 161) + (9*160)        Decimal:    0    1   2    3    4    5    6    7
= (15* 4096) + (10* 256) + (0* 16) + (9*1)        Hexa
                                                              8    9   A    B    C    D    E    F
= 61440+ 2560 + 0+9                               decimal:

= 64009 decimal                                   Decimal:    8    9   10   11   12   13   14   15


Hexadecimal to octal→
(FA09)₁₆=(64009)₈
 Decimal
              Operation      Quotient     Remainder          octal Result
 Number
 64009       ÷8=               8001           1              1
 8001        ÷8=               1000           1              11
 1000        ÷8=                125           0              011
 125         ÷8=                  15          5              5011
 15          ÷8=                   1          7              75011
 1           ÷8=                   0          1              175011

So, (FA09)₁₆ =(175011)₈
hexadecimal digit to obtain the equivalent
Hexadecimal to binary→
                                          group of four binary digits list:

Hexa
         F       A       0         9                   Hexa
decimal=                                                              0 1 2 3 4 5 6 7
                                                       decimal:
Binary=   1111 1010      0000      1001
      = 1111101000001001 binary
                                                                      0   0   0   0   0   0   0   0
                                                                      0   0   0   0   1   1   1   1
                                                       Binary:
                                                                      0   0   1   1   0   0   1   1
                                                                      0   1   0   1   0   1   0   1
  So,
     (FA09)₁₆=(111101000001001)₂                       Hexa
                                                                8 9 A B C DE F
                                                       decimal:

                                                                  1   1   1       1   1   1   1   1
                                                                  0   0   0       0   1   1   1   1
                                                       Binary:
                                                                  0   0   1       1   0   0   1   1
                                                                  0   1   0       1   0   1   0   1

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Cse

  • 1. CSE Assignment Name: Md. Raihan Dept: CSE Course: cse105 ID: 2012-2-60-040 sce: 4
  • 2. (111000110010)₂ conversion base2 to base8 conversion Equivalent value list Binary to octal→ binary Octal base2(binary)= 111000110010 base8(octal)= 7062 oct 000 0 So, (111000110010)₂=(7062)₈ 001 1 binary to decimal→ Base8(octal)= 7062 010 2 = 7*8³+0*8²+6*8¹+2*8° 011 3 = 3634 dec So, (111000110010)₂=(3634)₁₀ 100 4 binary to hexadecimal → 101 5 remainder 3634/16= 227 2 in hexadecimal form 110 6 227/16 = 14 3 in hexademal form 14/16 = 0 14=E in hexadecimal form 111 7 So,(111000110010)₂=(E32)₁₆
  • 3. (70642)₈ conversion Octal to decimal→ Oct= 76042 = 7*8´+6*8³+0*8²+4*8¹+2*8° = 31778 dec So, (76042)₈= (31778)₁₀ Decimal Operation Quotient Remainder Binary Result Number octal to binary→ 31778 ÷2= 15889 0 0 15889 ÷2= 7944 1 10 7944 ÷2= 3972 0 010 3972 ÷2= 1986 0 0010 1986 ÷2= 993 0 00010 993 ÷2= 496 1 100010 496 ÷2= 248 0 0100010 248 ÷2= 124 0 00100010 124 ÷2= 62 0 000100010 62 ÷2= 31 0 0000100010 31 ÷2= 15 1 10000100010 15 ÷2= 7 1 110000100010 7 ÷2= 3 1 1110000100010 3 ÷2= 1 1 11110000100010 1 ÷2= 0 1 111110000100010
  • 4. Octal to hexadecimal→ (76042)₈= (31778)₁₀ Decimal operation quotient remainder number 31778 ÷16 = 1986 2 1986 ÷16= 124 2 124 ÷16 = 7 12=C 7 ÷16= 0 7 0 Done. So, (76042)₈=(7C22)₁₆
  • 5. (786)₁₀ conversion Decimal to binary→ Decimal operation quotient remainder Binary result number 786 ÷2= 393 0 0 393 ÷2= 196 1 10 196 ÷2= 98 0 010 98 ÷2= 49 0 0010 49 ÷2= 24 1 10010 24 ÷2= 12 0 010010 12 ÷2= 6 0 0010010 6 ÷2= 3 0 00010010 3 ÷2= 1 1 100010010 1 ÷2= 0 1 1100010010 So, (786)₁₀=(1100010010)₂
  • 6. Decimal to octal→ Decimal Octal Operation Quotient Remainder Number Result 786 ÷8= 98 2 2 98 ÷8= 12 2 22 12 ÷8= 1 4 422 1 ÷8= 0 1 1422 0 done. So, (786)₁₀ = (1422)₈ Decimal to hexadecimal→ Decimal Hexadecimal Operation Quotient Remainder Number Result 786 ÷ 16 = 49 2 2 49 ÷ 16 = 3 1 12 3 ÷ 16 = 0 3 312=3C 0 done. So, (786)₁₀= (312)₁₆ =(3C)₁₆
  • 7. FA09 conversion Hexa-decimal value list: Hexa-dec to decimal→ FA09 hexadecimal: Hexa 0 1 2 3 4 5 6 7 decimal: = ((F)*163) + ((A)*162) + (0*161) + (9*160) = (15*163) + (10*162) + (0* 161) + (9*160) Decimal: 0 1 2 3 4 5 6 7 = (15* 4096) + (10* 256) + (0* 16) + (9*1) Hexa 8 9 A B C D E F = 61440+ 2560 + 0+9 decimal: = 64009 decimal Decimal: 8 9 10 11 12 13 14 15 Hexadecimal to octal→ (FA09)₁₆=(64009)₈ Decimal Operation Quotient Remainder octal Result Number 64009 ÷8= 8001 1 1 8001 ÷8= 1000 1 11 1000 ÷8= 125 0 011 125 ÷8= 15 5 5011 15 ÷8= 1 7 75011 1 ÷8= 0 1 175011 So, (FA09)₁₆ =(175011)₈
  • 8. hexadecimal digit to obtain the equivalent Hexadecimal to binary→ group of four binary digits list: Hexa F A 0 9 Hexa decimal= 0 1 2 3 4 5 6 7 decimal: Binary= 1111 1010 0000 1001 = 1111101000001001 binary 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 Binary: 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 So, (FA09)₁₆=(111101000001001)₂ Hexa 8 9 A B C DE F decimal: 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 Binary: 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1