Universidad Abierta y a Distancia de Mxico

Nombre de la Actividad: Actividad 2 Conversiones numricas entre sistemas decimal, binario, octal y hexadecimal.

Curso:Matemticas Discretas

Docente tutor: F. Javier Adalberto Palomar MayetDocente titular: Lic. Adelaida Romero Mendoza

Alumno (a):

18 de Abril de 2015

Cul es la representacin binaria, octal y hexadecimal de la superficie en kilmetros de la Repblica Mexicana?Superficie de la Repblica Mexicana 1, 964,375 km2Binario111011111100101010111

Octal7374527

Hexadecimal1DF957

(1964375)10 = (111011111100101010111)2(1964375)10 = (7374527)8

(1964375)10 = (1DF957)16

1964375/2=982187 r 11964375/8=245546 r 71964375/16=122773 r 7

982187/2=491093 r 1245546/8=30693 r 2122773/16=7673 r 5

491093/2=245546 r 130693/8=3836 r 57673/16=479 r 9

245546/2=122773 r 03836/8=479 r 4479/16=29 r F

122773/2=61381 r 1479/8=59r 729/16=1r D

61381/2=30693 r 059/8=7r 31/16=0r 1

30693/2=15346 r 17/8=0r 7

15346/2=7673 r 0

7673/2=3836 r 18x245546=196436816x122773=1964368

3836/2=1918 r 01964375-1964368=71964375-1964368=7

1918/2=959r 0

959/2=479r 18x30693=24554416x7673=122768

479/2=239r 1245546-245544=2122773-122768=5

239/2=119r 1

119/2=59r 18x3836=3068816x479=7664

59/2=29r 130693-30688=57673-7664=9

29/2=14r 1

14/2=7r 08x479=383216x29=464

7/2=3r 13836-3832=4479-464=15

3/2=1r 1

1/2=0r 18x59=47216x1=16

479-472=729-16=13

8x7=5616x0=0

59-56=31-0=1

8x0=010 11 12 13 14 15

7-0=7A B C D E F

Convierte los siguientes nmeros decimales, binarios, octales y hexadecimales a los sistemas numricos que se indican con su respectiva comprobacin.

NmeroConvertir a

1. (516) 10Binario

2. (4721) 10Octal

3. (961) 10Hexadecimal

4. (10010011) 2Decimal

5. (11001001) 2Octal

6. (10111010) 2Hexadecimal

7. (721) 8Decimal

8. (435) 8Binario

9. (64) 8Hexadecimal

10. (EB2) 16Binario

11. (D2) 16Decimal

12. (49A) 16Octal

2102928272625242322212010245122561286432168421010000001001. (516)10 516-512 4 -4 0

1. (516)10 = (1000000100)22. (4721)10 = (11161)8

3. (961)10 = (3C1)16

516/2=258 r 04721/8=590.125 0.125x8 r 1961/16=60.0625 0.0625x16=1r 1

258/2=129 r 0590/8=73.75 0.75x8 r 660/16=3.75 0.75x16=12r C

129/2=64 r 173/8=9.125 0.125x8 r 13r 3

64/2=32 r 09/8=1.125 0.125x8 r 110 11 12 13 14 15

32/2=16 r 01/8=0.125 0.125x8r 1 A B C D E F

16/2=8 r 0Forma 2Forma 2

8/2=4 r 04721/2=2360 r 1961/2=480r 1

4/2=2 r 02360/2=1180 r 0480/2=240r 0

2/2=1 r 01180/2=590 r 0240/2=120r 0

1/2=0 r 1590/2=295 r 0120/2=60r 0

295/2=147 r 160/2=30r 0

147/2=73r 130/2=15r 0

73/2=36r 115/2=7r 1

36/2=18r 07/2=3r 1

18/2=9r 03/2=1r 1

9/2=4r 11/2=0r 1

4/2=2r 0

2/2=1r 0

1/2=0r 1

1 001 001 110 001 binario0011 1100 0001 binario

1 1 1 6 1 octal 3 C 1 hexadecimal

4. (10010011) 2 = (147)105. (11001001) 2 = (311)8

6. (10111010) 2 = (BA)16

1x27+0x26+0x25+1x24+0x23+0x22+1x21+1x20011 001 0011011 1010

1x128+0x64+0x32+1x16+0x8+0x4+1x2+1x1 3 1 1 B A

128+0+0+16+0+0+2+1TablaTabla

147000 001 010 011 100 101 110 1111010 1011 1100 1101 1110 1111

0 1 2 3 4 5 6 7 A B C D E F

Forma 2Forma 2

1x27+1x26+0x25+0x24+1x23+0x22+0x21+1x201x27+0x26+1x25+1x24+1x23+0x22+1x21+0x20

1x128+1x64+0x32+0x16+1x8+0x4+0x2+1x11x128+0x64+1x32+1x16+1x8+0x4+1x2+0x1

128+64+0+0+8+0+0+1128+0+32+16+8+0+2+0

201186

201/8=25 r 1186/16=11r 10

25/8=3 r 111r 11

3 r 3

10 11 12 13 14 15

A B C D E F

7. (721) 8 = (465)108. (435) 8 = (100011101)2

9. (64) 8 = (34)16

7x82+2x81+1x80=7x64+2x8+1x1100011101 (0011 0100)2

448+16+1=465Tabla 4 2 1

(465)10 = (111010001)2000 001 010 011 100 101 110 1110000 0001 0010 0011 0100 0101 0110 0111

465/2=232 r 1 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

232/2=116 r 01000 1001 1010 1011 1100 1101 1110 1111

116/2=58 r 0 8 9 A B C D E F

58/2=29 r 0

29/2=14 r 1Forma 2Forma 2

14/2=7 r 04x82+3x81+5x80=4x64+3x8+5x16x81+4x80=6x8+4x1

7/2=3 r 1 256+24+5=285 48+4=52

3/2=1 r 1(285)10(52)10

1/2=0 r 1285/2=142r 152/2=26r 0

142/2=71r 026/2=13r 0

71/2=35r 1 13/2=6r 1

35/2=17r 1 6/2=3r 0

17/2=8r 13/2=1r 1

8/2=4r 01/2=0r 1

4/2=2r 0

2/2=1r 00011 0100 binario

1/2=0r 1 3 4 hexadecimal

10. (EB2)16 = (111010110010)211. (D2)16 = (210)10

12. (49A)16 = (2232)8 421

hexadecimal 8 4 2 1 binario10 11 12 13 14 15hexadecimal a binario

0000 0001 0010 0011 0100 0101 0110 0111 A B C D E F0000 0001 0010 0011 0100 0101 0110 0111

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

1000 1001 1010 1011 1100 1101 1110 1111161=16 160=1 1X2=2 16X13=2081000 1001 1010 1011 1100 1101 1110 1111

8 9 A B C D E F 2+208=210 8 9 A B C D E F

10 11 12 13 14 15(10010011010)2

A B C D E F010 010 011 010

2 2 3 2

Forma 2

14x162+11x161+2x160Forma 2

14x256+11x16+2x14x162+9x161+10x160

3584+176+2=37624x256+9x16+10x1

(3762)101024+144+10

3762/2=1881r 0(1178)10

1881/2=940r 11178/8=147r 2

940/2=470r 0147/8=18r 3

470/2=235r 018/8=2r 2

235/2=117r 12r 2

117/2=58r 1

58/2=29r 0

29/2=14r 1

14/2=7r 0

7/2=3r 1

3/2=1r 1

1/2=0r 1