Conversión entre Sistemas de Numeración: Binario, Decimal, Octal y Hexadecimal

1. Conversión de Decimal a Binario

a) 15,34(10

Parte entera

15(10 = 1111(2

Parte fraccionaria

0,34 * 2 = 0,68
0,68 * 2 = 1,36
0,36 * 2 = 0,72
0,72 * 2 = 1,44
0,44 * 2 = 0,88
0,88 * 2 = 1,76

0,34(10 = 0,010101(2

15,34(10 = 1111,010101(2

b) 77,25(10

Parte entera

77(10 = 1001101(2

Parte fraccionaria

0,25 * 2 = 0,5
0,5 * 2 = 1,0

0,25(10 = 0,01(2

77,25 (10 = 1001101,01(2

2. Conversión de Binario a Decimal

a) 1001011,1101(2

1*26 + 0*25 + 0*24 + 1*23 + 0*22 + 1*21 + 1*20 + 1*2-1 + 1*2-2 + 0*2-3 + 1*2-4 =

= 64 + 0 + 0 + 8 + 0 + 2 + 1 + 0,5 + 0,25 + 0 + 0,0625 =

= 75,8125(10

b) 11011,101(2

1*24 + 1*23 + 0*22 + 1*21 + 1*20 + 1*2-1 + 0*2-2 + 1*2-3 =

= 16 + 8 + 0 + 2 + 1 + 0,5 + 0 + 0,125 =

= 27,625 (10

3. Conversión de Decimal a Octal

a) 32,1875(10

Parte entera

32 |8_
0 4

32(10 = 40(8

Parte fraccionaria

0,1875 * 8 = 1,5
0,5 * 8 = 4,0

0,1875(10 = 0,14 (8

32,1875(10 = 40,14(8

b) 125,126953125(10

Parte entera

125 |8_
5 15 |8_
7 1

125(10 = 175(8

Parte fraccionaria

0,126953125 * 8 = 1,015625
0,015625 * 8 = 0,125
0,125 * 8 = 1,0

0,126953125(10 = 0,101(8

125,126953125(10 = 175,101(8

4. Conversión de Octal a Decimal

a) 32,1775(8

3*81 + 2*80 + 1*8-1 + 7*8-2 + 7*8-3 + 5*8-4 =

= 24 + 2 + 0 ,125 + 0,109375 + 0,013671875 + 0,001220703125 =

= 26,249267578125(10

b) 125,12(8

1*82 + 2*81 + 5*80 + 1*8-1 + 2*8-2 =

= 64 + 16 + 5 + 0,125 + 0,03125 =

= 85,15625(10

5. Conversión de Decimal a Hexadecimal

a) 57,062744140625(10

Parte entera

57 |16_
9 3

57(10 = 39(16

Parte fraccionaria

0,062744140625 * 16 = 1,00390625
0, 00390625 * 16 = 0,0625
0,0625 * 16 = 1,0

0,062744140625(10 = 0,101(16

57,062744140625(10 = 39,101(16

b) 14,0625(10

Parte entera

14(10 = E(16

Parte fraccionaria

0,0625 * 16 = 1,0

0,0625(10 = 0,1 (16

14,0625 (10 = E,1 (16

6. Conversión de Hexadecimal a Decimal

a) 25,AC1(16

2*161 + 5*160 + A*16-1 + C*16-2 + 1*16-3 =

= 32 + 5 + (10/16) + (12/162) + (1/163) =

= 32 + 5 + 0,625 + 0,046875 + 0,000244140625 =

= 37,672119140625(10

b) 1FB,A1(16

1*162 + F*161 + B*160 + A*16-1 + 1*16-2 =

= 256 + 15*16 + 11 + (10/16) + (1/162) =

= 256 + 240 + 11 + 0,625 + 0,00390625 =

= 507,62890625(10

7. Conversión de Octal a Hexadecimal

a) 32,1775(8

3 2 , 1 7 7 5
011 010 , 001 111 111 101
0001 1010 , 0011 1111 1101
1 10 , 3 15 13
1 A , 3 F D

32,1775(8 = 1A,3FD (16

b) 125,21(8

1 2 5 , 2 1
001 010 101 , 010 001
101 0101 , 0100 0100
5 5 , 4 4

125,21(8 = 55,44(16

8. Conversión de Hexadecimal a Octal

a) 32,1775(16

3 2 , 1 7 7 5
0011 0010 , 0001 0111 0111 0101
110 010 , 000 101 110 111 010 100
6 2 , 0 5 6 7 2 4

32,1775(16 = 62,056724(8

b) 125,21(16

1 2 5 , 2 1
0001 0010 0101 , 0010 0001
000 100 100 101 , 001 000 010
0 4 4 5 , 1 0 2

125,21(16 = 445,102(8

9. Representaciones de Números Enteros

a) 25(10

25(10=00011001  Signe i magnitud, complement a 1 i complement a 2

n=8  S = 27 = 128

25(10 + 128(10 = 153(10 = 10011001(e  Representació esbiaixada o excés a 2n-1

b) -25(10

10011001  Signe i magnitud

00011001  11100110 complement a 1

11100110
+1
11100111  11100111 complement a 2

-25(10 + 128(10 = 103(10 = 01100111(e  Representació esbiaixada o excés a 2n-1

c) 12(10

12(10=00001100 (2  Signe i magnitud, complement a 1 i complement a 2

n=8  S = 27 = 128

12(10 + 128(10 = 140(10 = 10001100(e  Representació esbiaixada o excés a 2n-1

d) -12(10

10001100  Signe i magnitud

00001100  11110011 complement a 1

11110011
+1
11110100  11110100 complement a 2

-12(10 + 128(10 = 116(10 = 01110100 (e  Representació esbiaixada o excés a 2n-1