Contoh Penyelesaian Soal Sistem Bilangan dan Konversi

A. Konversi
1. (125.4375)10 = (………………)2
2 125 1 0.475 x2 = 0. 875
2 62 0 0.875 x2 = 1. 75
2 31 1 0.57 x2 = 1. 5
2 15 1 0.5 x2 = 1
2 7 1 = 1110
2 3 1
1
= 1111101
Hasil = (1111101.1110)2

2. ( A F B D)16 = (………………)10
= (10x163)+(15x162)+(11x161)+(13x160)
= (40960+3840+176+13)
= (44989)10

3. (011111101110101110)2 = (………………)8
011 111 101 110 101 110
2 7 5 6 5 6
Hasil = ( 2 7 5 6 5 6 )8

4. ( 3 2 4)8 = (………………)16
( 3 2 4)8 = ( 011010100)2
= 0000 1101 0100
0 13 4
= ( 0 D 4)16






A. Aritmatika
5. ( B D A 0)16 + ( F C B 9 )16 = (………………)16
= B D 6 A
F C B 9 +
27 26 18 19
16 16 16 16 -
1 11 10 2 3
= ( 1 B A 2 3 )16

6. ( 6 9 )8 + (86)10 = (………………)2
( 6 9 )10 = ( 110 1001 )2
(86)10 = ( 101 0110 )2
2 86 0
2 43 1
2 21 1
2 10 0
2 5 1
2 2 0
1

= 110 1001
101 0110 +
211 1111
2 -
= ( 1 011 1111 )2







7. ( 1101 0011)2 – ( A 8 )16 = (………………)10
( 1101 0011)2 = ( D 3)16
( D 3 )16 = ( 13x161) + (3x160)
= ( 208 + 3)
= 211
(A 8 )16 = ( 10x161) + (8x160)
= ( 160 + 8 )
= 168
(211)10 – (168)10 = 211
168 -
= (43)10

B. Logika
8. ( F A D 0 )16 AND ( 4 7 3 )8 = (………………)16
( F A D 0 )16 = ( 1111 1010 1101 0000)2
( 4 7 3 )8 = (0001 0011 1011)2 Z
(1111 0000 0001 0000)2
= ( F 0 1 0)16
9. ( 1101 0011)2 OR ( 8 9 )8 = (………………)16
( 8 9 )8 = ( 1000 1001 )2
1101 0011
1000 1001 +
1 2101 1122
2 22 -
(1 0101 1100)2
= ( 1 5 C )16









10. ( 0011 0101 )2 AND (83)10 = (………………)16
(83)10 =
2 86 0
2 43 1
2 21 1
2 10 0
2 5 1
2 2 0
1
= ( 1010011)2
0011 0101
101 0011 Z
0001 0001
= ( 1 1)16