Sistem Sistem Bilangan, Operasi dan Kode
Tujuan Topik Bahasan
- Mengulas kembali sistem bilangan desimal.
- Menghitung dalam bentuk bilangan biner.
- Memindahkan dari bentuk bilangan desimal ke biner dan dalam biner ke dalam desimal.
- Penggunaan operasi aritmatika pada bilangan biner.
- Menentukan komplemen 1 dan 2 dari sebuah bilangan biner.
- Dan lain - lainnya …… ..
Sistem Bilangan
Sistem Biner dan Kode - kode digital merupakan dasar untuk komputer dan elektronika digital secara umum. Sistem bilangan biner seperti desimal, hexadesimal dan oktal juga dibahas pada bagian ini. Operasi aritmatika dengan bilangan biner akan dibahas untuk memberikan dasar pengertian bagaimana komputer dan jenis perangkat digital lain bekerja.
Bilangan Desimal
- Dalam setiap bilangan desimal terdiri dari 10 digit, 0 sampai dengan 9
- Ungkapkan bilangan desimal 2745.214 sebagai penjumlahan nilai setiap digit.
Bilangan Biner
- Sistem Bilangan biner merupakan cara lain untuk melambangkan kuantitas, dimana 1 (HIGH) dan 0 (LOW).
- Sistem bilangan biner mempunyai nilai basis 2 dengan nilai setiap posisi dibagi dengan faktor 2:
c
Konversikan seluruh bilangan biner 1101101 ke desimal
Hasil:
Nilai : 26 25 24 23 22 21 20
Biner : 1 1 0 1 1 0 1
1101101 = 26 + 25 + 23 + 22 + 20
= 64 + 32 + 8 + 4 + 1 = 109
Konversi Desimal ke Biner
- Metode Sum-of-Weight.
- Pengulangan pembagian dengan Metode bilangan 2.
- Konversi fraksi desimal ke biner.
Metode Sum-of-Weight
Binary Arithmetic
- Binary arithmetic is essential in all digital computers and in many other types of digital systems.
- Addition, Subtraction, Multiplication, and Division
Binary Addition
0+0=0 sum of 0 with a carry of 0
1 x 1 = 1
0+1=1 sum of 1 with a carry 0f 0
1+0=1 sum of 1 with a carry of 0
1+1=10 sum of 0 with a carry 0f 1
Binery Subtraction
The four basic rules for subtracting bits are as follows:
0-0=0
1-1=0
1-0=0
10-1=1 0-1 with a borrow of 1
Binery Multiplication
The four basic rules for multiplying bits are as follows:
0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1
Binery Division
Division in binary follows the same procedure as division in decimal.
1’s and 2’s Complements of Binary Numbers
- The 1’s and 2’s Complements of Binary Numbers are very important because they permit the representation of negative numbers
- The method of 2’s compliment arithmetic is commonly used in computers to handle negative numbers
Finding the 1’s Complement
The 1’s complement of a binary number is found by changing all 1s to 0s and all 0s to 1s.
1 0 1 1 0 0 1 0 (Binary Number)
0 1 0 0 1 1 0 1 (1’s Complement)
Finding the 2 compliment
The 2’s complement of a binary number is found by adding 1 to the LSB of the 1’s complement
Hexadecimal Numbers
- Most digital systems deal with groups of bits in even powers of 2 such as 8, 16, 32, and 64 bits.
- Hexadecimal uses groups of 4 bits.
- Base 16
- 16 possible symbols
- 0 - 9 and A - F
- Allows for convenient handling of long binary strings.
Hexadecimal Numbers
- Convert from hex to decimal by multiplying each hex digit by its positional weight.
- Hexadecimal is useful for representing long strings of bits.
- Understanding the conversion process and memorizing the 4 bit patterns for each hexadecimal digit will prove valuable later.
BCD
- Binary Coded Decimal (BCD) is another way to present decimal numbers in binary form.
- BCD is widely used and combines features of both decimal and binary systems.
- Each digit is converted to a binary equivalent.
- BCD is not a number system.
- BCD is a decimal number with each digit encoded to its binary equivalent.
- A BCD number is not the same as a straight binary number.
- The primary advantage of BCD is the relative ease of converting to and from decimal.
Nama :Yogga Tolly Dewanto
Nim :2003015136
Kelas :2F
sumber:"https://onlinelearning.uhamka.ac.id"
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