digital system and binary numbers (2'nd update)
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Sistem DigitalNugroho Adi P
nugnux@gmail.comAravir@me.com
Thursday, September 4, 14
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One characteristic of digital systems is their ability to represent and manipulate discrete elements of information.
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Discrete InformationHuruf
Kartu
Power Ranger
Kotak Papan Catur
Jumlah Mahasiswa
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Discrete Information26 Huruf
52 Kartu
6 Power Ranger
64 Kotak Papan Catur
33 Mahasiswa
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Elemen informasi diskrit diwakili di sistem digital oleh sinyal
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arus,
tegangan
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Sinyal diskrit hanya mempunyai dua nilai
(Biner)
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Bit bernilai 0 dan 1
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Discrete elements of information are represented with groups of bits called binary codes
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contoh kode biner
1:
2:
3:
4:
5:
0001
0010
0011
0100
0101
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Kadang
(1000)2 ≠ (1000)10
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tidak mungkin
(1008)2
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tidak mungkin keliru
00F1
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a digital system is a system that manipulates discrete elements of information represented internally in binary form.
Thus
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Diskrit secara alami
Diambil dari proses kontinu (kuantisasi)
Informasi Diskrit
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Diskrit alami
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Kuantisasi
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Thursday, September 4, 14
Kenapa Digital?
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Dapat diprogram
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Satu alat dapat digunakan untuk bermacam keperluan
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Bilangan Biner
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1395
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1395
seribu tiga ratus sembilan puluh lima
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1395
seribu tiga ratus sembilan puluh lima
1000 + 300 + 90 + 5
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1395
seribu tiga ratus sembilan puluh lima
1000 + 300 + 90 + 5
1 x 1000 + 3 x 100 + 9 x 10 + 5
Thursday, September 4, 14
1395
seribu tiga ratus sembilan puluh lima
1000 + 300 + 90 + 5
1 x 1000 + 3 x 100 + 9 x 10 + 5
1 x 103 + 3 x 102 + 9 x 101 + 5 x 100
Thursday, September 4, 14
1395
seribu tiga ratus sembilan puluh lima
1000 + 300 + 90 + 5
1 x 1000 + 3 x 100 + 9 x 10 + 5
1 x 103 + 3 x 102 + 9 x 101 + 5 x 100
4 bit
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1 x 103 + 3 x 102 + 9 x 101 + 5 x 100
a3 x 103 + a2 x 102 + a1 x 101 + a0 x 100
basis 10
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basis 10 secara umum
...+103a3 + 102a2 + 101a1 + 100a0 + 10-1a-1 + 10-2a-2 + 10-3a-3 + ...
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secara umum hanya ditulis koefisennya saja
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Biner
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Biner
...+23a3 + 22a2 + 21a1 + 20a0 + 2-1a-1 + 2-2a-2 + 2-3a-3 + ...
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Biner
...+23a3 + 22a2 + 21a1 + 20a0 + 2-1a-1 + 2-2a-2 + 2-3a-3 + ...
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Biner
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Biner
1101
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Biner
1101
1 x 23 + 1 x 22 + 0 x 21 + 1 x 20
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Biner
1101
1 x 23 + 1 x 22 + 0 x 21 + 1 x 20
8 + 4 + 0 + 1 (desimal)
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Biner
1101
1 x 23 + 1 x 22 + 0 x 21 + 1 x 20
8 + 4 + 0 + 1 (desimal)
13 (desimal)
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Biner
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Biner
10.1
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Biner
10.1
1 x 21 + 0 x 20 + 1 x 2-1
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Biner
10.1
1 x 21 + 0 x 20 + 1 x 2-1
2 + 0 + 0.5 (desimal)
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Biner
10.1
1 x 21 + 0 x 20 + 1 x 2-1
2 + 0 + 0.5 (desimal)
2.5 (desimal)
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Basis-r
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Basis-r
...+r3a3 + r2a2 + r1a1 + r0a0 + r-1a-1 + r-2a-2 + r-3a-3 + ...
Thursday, September 4, 14
Basis-r
...+r3a3 + r2a2 + r1a1 + r0a0 + r-1a-1 + r-2a-2 + r-3a-3 + ...
nilai ai antara 0 dan r-1
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oktal
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oktal
10.1
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oktal
10.1
1 x 81 + 0 x 80 + 1 x 8-1
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oktal
10.1
1 x 81 + 0 x 80 + 1 x 8-1
8 + 0 + 0.125 (desimal)
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oktal
10.1
1 x 81 + 0 x 80 + 1 x 8-1
8 + 0 + 0.125 (desimal)
8.125 (desimal)
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Thursday, September 4, 14
hexadesimal
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hexadesimal
10.1
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hexadesimal
10.1
1 x 161 + 0 x 160 + 1 x 16-1
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hexadesimal
10.1
1 x 161 + 0 x 160 + 1 x 16-1
16 + 0 + 0.125 (desimal)
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hexadesimal
10.1
1 x 161 + 0 x 160 + 1 x 16-1
16 + 0 + 0.125 (desimal)
16.0625 (desimal)
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Biner
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Biner
210 = 1024 = 1K
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Biner
210 = 1024 = 1K
220 = M
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Biner
210 = 1024 = 1K
220 = M
230 = G
Thursday, September 4, 14
Biner
210 = 1024 = 1K
220 = M
230 = G
240 = T
Thursday, September 4, 14
Biner
210 = 1024 = 1K
220 = M
230 = G
240 = T
Thursday, September 4, 14
Aritmatika bilangan berbasis r mengikuti aturan yang sama dengan bilangan desimal
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Biner
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Biner
11 + 0 = 11
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Biner
11 + 0 = 11
1+1 = 10
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Biner
11 + 0 = 11
1+1 = 10
10+11= 101
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Biner
11 + 0 = 11
1+1 = 10
10+11= 101
11+11 = 110
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Thursday, September 4, 14
octal
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octal
1 + 1 = 2
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octal
1 + 1 = 2
7 + 1 = 10
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octal
1 + 1 = 2
7 + 1 = 10
17 +11 = 30
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octal
1 + 1 = 2
7 + 1 = 10
17 +11 = 30
17 + 1 = 20
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hexadesimal
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hexadesimal
9 + 1 = A
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hexadesimal
9 + 1 = A
9 + 2 = B
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hexadesimal
9 + 1 = A
9 + 2 = B
F + 2 = 11
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hexadesimal
9 + 1 = A
9 + 2 = B
F + 2 = 11
FF + 1 = 100
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Biner
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Biner
1 - 1 = 0
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Biner
1 - 1 = 0
10 - 01 = 01
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Biner
1 - 1 = 0
10 - 01 = 01
1011 - 1001 =0010
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Octal
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Octal
10 - 1 = 7
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Octal
10 - 1 = 7
17 - 10 = 7
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Octal
10 - 1 = 7
17 - 10 = 7
21 - 17 = 2
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Hexadesimal
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Hexadesimal
10 - 1 = F
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Hexadesimal
10 - 1 = F
1A - 11 = 9
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Hexadesimal
10 - 1 = F
1A - 11 = 9
A0 - 1 = 9F
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Konversi
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Konversi
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Konversi
(1)2 = (1)8 = (1)16 = (1)5 = 1 (desimal)
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Konversi
(1)2 = (1)8 = (1)16 = (1)5 = 1 (desimal)
(1 0000)2 = (20)8 = (10)16 = (31)5 = 16 (desimal)
Thursday, September 4, 14
Konversi
(1)2 = (1)8 = (1)16 = (1)5 = 1 (desimal)
(1 0000)2 = (20)8 = (10)16 = (31)5 = 16 (desimal)
(0.000110...)2 = 0.05 (desimal)
Thursday, September 4, 14
Konversi
(1)2 = (1)8 = (1)16 = (1)5 = 1 (desimal)
(1 0000)2 = (20)8 = (10)16 = (31)5 = 16 (desimal)
(0.000110...)2 = 0.05 (desimal)
(0.001)2 = 0.125 (desimal)
Thursday, September 4, 14
Thursday, September 4, 14
Desimal ke binary
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Desimal ke binary102
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Desimal ke binary102102 bagi dua
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Desimal ke binary102102 bagi dua51 sisa 0
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 1
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 1
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 0
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 1
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah1100110
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah1100110jadi
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah1100110jadi (102)10 = (1100110)2
Thursday, September 4, 14
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah1100110jadi (102)10 = (1100110)2
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Thursday, September 4, 14
Desimal ke octal
Thursday, September 4, 14
Desimal ke octal102
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Desimal ke octal102102 bagi delapan
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Desimal ke octal102102 bagi delapan12 sisa 6
Thursday, September 4, 14
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 4
Thursday, September 4, 14
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 40 sisa 1
Thursday, September 4, 14
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 40 sisa 1
Thursday, September 4, 14
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 40 sisa 1
jadi
Thursday, September 4, 14
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 40 sisa 1
jadi
(102)10 = (146)2
Thursday, September 4, 14
Thursday, September 4, 14
Desimal ke heksadesimal
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Desimal ke heksadesimal102
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Desimal ke heksadesimal102102 bagi enambelas
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Desimal ke heksadesimal102102 bagi enambelas6 sisa 6
Thursday, September 4, 14
Desimal ke heksadesimal102102 bagi enambelas6 sisa 60 sisa 6
Thursday, September 4, 14
Desimal ke heksadesimal102102 bagi enambelas6 sisa 60 sisa 6jadi
Thursday, September 4, 14
Desimal ke heksadesimal102102 bagi enambelas6 sisa 60 sisa 6jadi (102)10 = (6)16
Thursday, September 4, 14
Thursday, September 4, 14
Pecahan
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Pecahan(0.2)10
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Pecahan(0.2)10
0.2 x 2 = 0.4 + 0
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 1
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 1
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 1
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 1
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0.....
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0.....(0.22)10 = (0.0011001100...)2
Thursday, September 4, 14
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0.....(0.22)10 = (0.0011001100...)2
Thursday, September 4, 14
Thursday, September 4, 14
Pecahan
Thursday, September 4, 14
Pecahan(0.25)10
Thursday, September 4, 14
Pecahan(0.25)10
0.25 x 2 = 0.5 + 0
Thursday, September 4, 14
Pecahan(0.25)10
0.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
Thursday, September 4, 14
Pecahan(0.25)10
0.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1 .....
Thursday, September 4, 14
Pecahan(0.25)10
0.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1 .....(0.25)10 = (0.01)2
Thursday, September 4, 14
Pecahan(0.25)10
0.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1 .....(0.25)10 = (0.01)2
Thursday, September 4, 14
Thursday, September 4, 14
Pecahan
Thursday, September 4, 14
Pecahan(0.5)10
Thursday, September 4, 14
Pecahan(0.5)10
0.5 x 2 = 0.0 + 1
Thursday, September 4, 14
Pecahan(0.5)10
0.5 x 2 = 0.0 + 1
Thursday, September 4, 14
Pecahan(0.5)10
0.5 x 2 = 0.0 + 1
(0.5)10 = (0.1)2
Thursday, September 4, 14
Pecahan(0.5)10
0.5 x 2 = 0.0 + 1
(0.5)10 = (0.1)2
Thursday, September 4, 14
Thursday, September 4, 14
Pecahan
Thursday, September 4, 14
Pecahan(0.125)10
Thursday, September 4, 14
Pecahan(0.125)10
0.125 x 2 = 0.25 + 0
Thursday, September 4, 14
Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 0
Thursday, September 4, 14
Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
Thursday, September 4, 14
Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
Thursday, September 4, 14
Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
(0.5)10 = (0.001)2
Thursday, September 4, 14
Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
(0.5)10 = (0.001)2
Thursday, September 4, 14
Thursday, September 4, 14
Thursday, September 4, 14
Oktal dan Heksadesimal
Thursday, September 4, 14
Thursday, September 4, 14
(111111111111)2
Thursday, September 4, 14
(111111111111)2
(111 111 111 111)2 = (7 7 7 7)8
Thursday, September 4, 14
(111111111111)2
(111 111 111 111)2 = (7 7 7 7)8
(1111 1111 1111)2 = (F F F )16
Thursday, September 4, 14
Thursday, September 4, 14
Bilangan biner sulit untuk digunakan
Thursday, September 4, 14
Bilangan biner sulit untuk digunakan
Mengunakan digit yang lebih banyak dari desimal
Thursday, September 4, 14
Thursday, September 4, 14
Bilangan desimal lebih mudah digunakan
Thursday, September 4, 14
Bilangan desimal lebih mudah digunakan
namun komputer menggunakan biner
Thursday, September 4, 14
Bilangan desimal lebih mudah digunakan
namun komputer menggunakan biner
konversi desimal ke biner rumit
Thursday, September 4, 14
Octal dan Hexadecimal memperkecil digit
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Thursday, September 4, 14
Complements
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‘negatif ’-nya sebuah bilangan
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Thursday, September 4, 14
menyederhanakan pengurangan
Thursday, September 4, 14
menyederhanakan pengurangan
(dilakukan dengan penjumlahan)
Thursday, September 4, 14
menyederhanakan pengurangan
(dilakukan dengan penjumlahan)
hemat sirkuit
Thursday, September 4, 14
Thursday, September 4, 14
Komplemen bilangan berbasis-r
Thursday, September 4, 14
Komplemen bilangan berbasis-r
komplemen r (radix)
Thursday, September 4, 14
Komplemen bilangan berbasis-r
komplemen r (radix)
komplemen r-1 (diminished radix)
Thursday, September 4, 14
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki diminished radix komplemen (rn-1)-N
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki diminished radix komplemen (rn-1)-N
mis 7 desimal akan memiliki diminished radix komplemen (101-1)-7 = 2
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki diminished radix komplemen (rn-1)-N
mis 7 desimal akan memiliki diminished radix komplemen (101-1)-7 = 2
07 desimal akan memiliki diminished radix komplemen (102-1)-7 = 92
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki diminished radix komplemen (rn-1)-N
mis 7 desimal akan memiliki diminished radix komplemen (101-1)-7 = 2
07 desimal akan memiliki diminished radix komplemen (102-1)-7 = 92
Thursday, September 4, 14
Thursday, September 4, 14
diminised radix complement tuk binary
Thursday, September 4, 14
diminised radix complement tuk binary
100 -> (23-1)-100
Thursday, September 4, 14
diminised radix complement tuk binary
100 -> (23-1)-100
= (1000-1)-100
Thursday, September 4, 14
diminised radix complement tuk binary
100 -> (23-1)-100
= (1000-1)-100
= (111)-100
Thursday, September 4, 14
diminised radix complement tuk binary
100 -> (23-1)-100
= (1000-1)-100
= (111)-100
= 011
Thursday, September 4, 14
Thursday, September 4, 14
diminised radix complement tuk binary
Thursday, September 4, 14
diminised radix complement tuk binary
111 -> (23-1)-111
Thursday, September 4, 14
diminised radix complement tuk binary
111 -> (23-1)-111
= (1000-1)-111
Thursday, September 4, 14
diminised radix complement tuk binary
111 -> (23-1)-111
= (1000-1)-111
= (111)-111
Thursday, September 4, 14
diminised radix complement tuk binary
111 -> (23-1)-111
= (1000-1)-111
= (111)-111
= 000
Thursday, September 4, 14
Thursday, September 4, 14
diminised radix complement tuk binary
Thursday, September 4, 14
diminised radix complement tuk binary
101 -> (23-1)-101
Thursday, September 4, 14
diminised radix complement tuk binary
101 -> (23-1)-101
= (1000-1)-101
Thursday, September 4, 14
diminised radix complement tuk binary
101 -> (23-1)-101
= (1000-1)-101
= (111)-101
Thursday, September 4, 14
diminised radix complement tuk binary
101 -> (23-1)-101
= (1000-1)-101
= (111)-101
= 010
Thursday, September 4, 14
Thursday, September 4, 14
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki radix komplemen (rn)-N
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki radix komplemen (rn)-N
mis 7 desimal akan memiliki radix komplemen (101)-7 = 3
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki radix komplemen (rn)-N
mis 7 desimal akan memiliki radix komplemen (101)-7 = 3
07 desimal akan memiliki radix komplemen (102)-7 = 93
Thursday, September 4, 14
jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki radix komplemen (rn)-N
mis 7 desimal akan memiliki radix komplemen (101)-7 = 3
07 desimal akan memiliki radix komplemen (102)-7 = 93
Thursday, September 4, 14
Thursday, September 4, 14
radix complement tuk binary
Thursday, September 4, 14
radix complement tuk binary
100 -> (23)-100
Thursday, September 4, 14
radix complement tuk binary
100 -> (23)-100
= (1000)-100
Thursday, September 4, 14
radix complement tuk binary
100 -> (23)-100
= (1000)-100
= (1000)-100
Thursday, September 4, 14
radix complement tuk binary
100 -> (23)-100
= (1000)-100
= (1000)-100
= 100
Thursday, September 4, 14
Thursday, September 4, 14
radix complement tuk binary
Thursday, September 4, 14
radix complement tuk binary
111 -> (23)-111
Thursday, September 4, 14
radix complement tuk binary
111 -> (23)-111
= (1000)-111
Thursday, September 4, 14
radix complement tuk binary
111 -> (23)-111
= (1000)-111
= 001
Thursday, September 4, 14
Thursday, September 4, 14
radix complement tuk binary
Thursday, September 4, 14
radix complement tuk binary
101 -> (23-1)-101
Thursday, September 4, 14
radix complement tuk binary
101 -> (23-1)-101
= (1000)-101
Thursday, September 4, 14
radix complement tuk binary
101 -> (23-1)-101
= (1000)-101
= 011
Thursday, September 4, 14
Thursday, September 4, 14
Jika memiliki radix point, hilangkan!
Thursday, September 4, 14
Jika memiliki radix point, hilangkan!
Kembalikan lagi setelah hitungan
Thursday, September 4, 14
Thursday, September 4, 14
Pengurangan dengan komplemen
Thursday, September 4, 14
Pengurangan dengan komplemen
(lebih mudah bagi hardware)
Thursday, September 4, 14
Pengurangan dengan komplemen
(lebih mudah bagi hardware)
(tak ada pinjaman)
Thursday, September 4, 14
Thursday, September 4, 14
pengurangan bilangan M-N berdigit n berbasis r
Thursday, September 4, 14
pengurangan bilangan M-N berdigit n berbasis r
tambahkan M dengan radix komplemen dari N
Thursday, September 4, 14
pengurangan bilangan M-N berdigit n berbasis r
tambahkan M dengan radix komplemen dari N
M + ( rn - N ) = M - N + rn
Thursday, September 4, 14
Thursday, September 4, 14
jika M≥N maka penjumlahan akan menghasilkan (end carry)
Thursday, September 4, 14
jika M≥N maka penjumlahan akan menghasilkan (end carry)
buang end carry
Thursday, September 4, 14
jika M≥N maka penjumlahan akan menghasilkan (end carry)
buang end carry
yang tersisa merupakan hasilnya
Thursday, September 4, 14
Thursday, September 4, 14
Jika M < N, maka penjumlahan tidak menghasilkan end carry
Thursday, September 4, 14
Jika M < N, maka penjumlahan tidak menghasilkan end carry
hasilnya merupakan komplemen (N-M)
Thursday, September 4, 14
Jika M < N, maka penjumlahan tidak menghasilkan end carry
hasilnya merupakan komplemen (N-M)
agar ‘enak’ dilihat, ambil komplemen hasil penjumlahan
Thursday, September 4, 14
Jika M < N, maka penjumlahan tidak menghasilkan end carry
hasilnya merupakan komplemen (N-M)
agar ‘enak’ dilihat, ambil komplemen hasil penjumlahan
beri tanda negatif
Thursday, September 4, 14
Thursday, September 4, 14
Bilangan Biner Bertanda
(Signed Binary Number)
Thursday, September 4, 14
Thursday, September 4, 14
Tanda minus tak mungkin digunakan;
Thursday, September 4, 14
Tanda minus tak mungkin digunakan;
diganti dengan bit paling kiri
Thursday, September 4, 14
Thursday, September 4, 14
bilangan positif memiliki bit terkiri nol
Thursday, September 4, 14
bilangan positif memiliki bit terkiri nol
(0100)2 = +4
Thursday, September 4, 14
bilangan positif memiliki bit terkiri nol
(0100)2 = +4
(0111)2 = +7
Thursday, September 4, 14
Thursday, September 4, 14
bilangan positif memiliki bit terkiri satu
Thursday, September 4, 14
bilangan positif memiliki bit terkiri satu
(1100)2 = -4
Thursday, September 4, 14
bilangan positif memiliki bit terkiri satu
(1100)2 = -4
(1111)2 = -7
Thursday, September 4, 14
Hati-hati!
Thursday, September 4, 14
Thursday, September 4, 14
(1100)2 = -4 = 12
Thursday, September 4, 14
(1100)2 = -4 = 12
(1111)2 = -7 = 15
Thursday, September 4, 14
Pengguna harus tahu apakah sebuah bilangan biner yang sedang ditinjau itu bertanda atau tidak
Thursday, September 4, 14
Biasanya ada petunjuk, informasi atau definisi yang menyertai sebuah bilangan biner
(biasanya tidak ada masalah)
Thursday, September 4, 14
Biner Negatif
Thursday, September 4, 14
Biner Negatif
signed-magnitude representation
Thursday, September 4, 14
Biner Negatif
signed-magnitude representation
signed-1’s-complement representation
Thursday, September 4, 14
Biner Negatif
signed-magnitude representation
signed-1’s-complement representation
signed-2’s-complement representation
Thursday, September 4, 14
Signed-magnitude Representation
Thursday, September 4, 14
Signed-magnitude Representation
-4 = (-0100)2 =(1100)2 -> empat bit
Thursday, September 4, 14
Signed-magnitude Representation
-4 = (-0100)2 =(1100)2 -> empat bit
-4 = (-00100)2 =(10100)2 -> enam bit
Thursday, September 4, 14
Signed-magnitude Representation
-4 = (-0100)2 =(1100)2 -> empat bit
-4 = (-00100)2 =(10100)2 -> enam bit
-4 = (-00000100)2 = (10000100)2 -> delapan bit
Thursday, September 4, 14
Signed-1’s-Complement Representation
Thursday, September 4, 14
Signed-1’s-Complement Representation
-4 = (-0100)2 = (1011)2 -> empat bit
Thursday, September 4, 14
Signed-1’s-Complement Representation
-4 = (-0100)2 = (1011)2 -> empat bit
-4 = (-000100)2 = (111011)2 -> enam bit
Thursday, September 4, 14
Signed-1’s-Complement Representation
-4 = (-0100)2 = (1011)2 -> empat bit
-4 = (-000100)2 = (111011)2 -> enam bit
-4 = (-00000100)2 = (11111011)2 -> delapan bit
Thursday, September 4, 14
Signed-2’s-Complement Representation
Thursday, September 4, 14
Signed-2’s-Complement Representation
-4 = (-0100)2 = (1100)2 -> empat bit
Thursday, September 4, 14
Signed-2’s-Complement Representation
-4 = (-0100)2 = (1100)2 -> empat bit
-4 = (-000100)2 = (111100)2 -> enam bit
Thursday, September 4, 14
Signed-2’s-Complement Representation
-4 = (-0100)2 = (1100)2 -> empat bit
-4 = (-000100)2 = (111100)2 -> enam bit
-4 = (-00000100)2 = (11111100)2 -> delapan bit
Thursday, September 4, 14
Thursday, September 4, 14
Selesai
Dan dia hidup bahagia selama-lamanya...Thursday, September 4, 14
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