sistem bilangan dan format data -...
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Sistem Bilangan dan Format Data
Basis
• Basis suatu sistem bilangan adalah sembarang angka termasuk 0 yang ada dalam suatu sistem bilangan
• Macamnya :• Decimal (basis 10) : 0,1,2,3,4,5,6,7,8,9
• Biner (Basis 2) : 0,1
• Hexadecimal (basis 16) : 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
• Oktal (basis 8) : 0,1,2,3,4,5,6,7
Munculnya Sistem Bilangan
• Sistem bilangan muncul karena komputer melakukan operasi menggunakan suatu bilangan tertentu, yaitu biner.
• Semua kode program dan data disimpan dan dimanipulasi menggunakan sistembiner.
• Masing-masing digit dalam sistem biner disebut bit (binary digit) dan hanya mempunyai dua harga, 0 dan 1
• Bit biasanya disimpan dalam kelompok 8 bit disebut byte
16 bit disebut bye
Misalnya : 1100112 adalah :
• 1x25 + 1x24 + 0x23 + 0x22 + 1x21 + 1x20
Decimal
• Have a base, or radix of 10
• Each digit in the number is multiplied by 10 raised to a powercorresponding to the digit’s position
• Ex :
• 83
• 4728
• 10009
• 0.256
• 10009.1001
Decimal
• 83 = (8 x 101) + (3 x 100)
• 4728 = (4x103) + (7x102) + (2x101) + (8 x 100)
• 10009 = (1x104) + (0x103) + (0x102) +
= (0 x 101) + (9 x 100)
Decimal - Fractions
X = { …d2d1d0.d-1d-2d-3…}
Ex :
0.256 = (2x10-1) + (5x10-2) + (6x10-3)
10009.1001 ???
Binary
• Only 2 digits, 1 and 0
• Numbers in the binary system are represented to the base 2
• Ex :
• 0(2)
• 1(2)
• 0101(2)
• 1010(2)
Binary - Example
• 10(2) = (1 x 21) + (0 x 20)
= 2(10)
• 1111(2) = (1 x 23) + (1 x 22) + (1 x 21) + (1 x 20)
= 23 + 22 + 21 + 20
= 8 + 4 + 2 + 1
= 15(10)
Converting Between Binary and Decimal
• 3(10) = ………..(2)
• 24(10) = ………..(2)
• 255(10) = ………..(2)
Decimal to Binary
3(10) = …(2)
128 64 32 16 8 4 2 1
27 26 25 24 23 22 21 20
Decimal to Binary
3(10) = …(2)
3(10) = 11(2)
128 64 32 16 8 4 2 1
27 26 25 24 23 22 21 20
0 0 0 0 0 0 1 1
Decimal to Binary
24(10) = …(2)
24(10) = 11000(2)
128 64 32 16 8 4 2 1
27 26 25 24 23 22 21 20
0 0 0 1 1 0 0 0
Decimal to Binary
255(10) = …(2)
255(10) = 11111111(2)
128 64 32 16 8 4 2 1
27 26 25 24 23 22 21 20
1 1 1 1 1 1 1 1
Binary to Decimal
• 101(2) = ………..(10)
• 1001(2) = ………..(10)
• 1111(2) = ………..(10)
Binary to Decimal
101(2) = …(10)
1 0 1
Binary to Decimal
101(2) = …(10)
1 0 1
22 21 20
Binary to Decimal
101(2) = …(10)
101(2) = (1x22) + (0x21) + (1x20)
= 4 + 0 + 1
= 5(10)
1 0 1
22 21 20
4 0 1
Hexadecimal
• Binary digits are grouped into sets of four
• Base 16
Ex :
• 2C(16)
• DE2(16)
• A(16)
• AA(16)
• 69F(16)
Hexadecimal to Decimal
2C(16) = …(10)
2C(16) = (2x161) + (12x160)
= 32 + 12
= 44(10)