Tugas 2. Rangkuman Materi Sistem Bilangan
Tujuan Topik Bahasan
l Mengulas kembali sistem bilangan desimal.
l Menghitung
dalam bentuk bilangan biner.
l Memindahkan
dari bentuk bilangan desimal ke biner dan dalam biner ke dalam desimal.
l Penggunaan
operasi aritmatika pada bilangan biner.
l Menentukan
komplemen 1 dan 2 dari sebuah bilangan biner.
l Dan lain – lainnya……..
Pendahuluan
l
Sistem
Biner dan Kode – kode digital merupakan dasar untuk komputer dan elektronika
digital secara umum.
l
Sistem
bilangan biner seperti desimal, hexadesimal dan oktal juga dibahas pada bagian
ini.
l Operasi aritmatika dengan bilangan biner akan dibahas untuk memberikan dasar pengertian bagaimana komputer dan jenis – jenis perangkat digital lain bekerja.
Sistem Bilangan
Bilangan Biner
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Sistem
Bilangan biner merupakan cara lain untuk melambangkan kuantitas, dimana 1
(HIGH) dan 0 (LOW).
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Sistem
bilangan biner mempunyai nilai basis 2 dengan nilai setiap posisi dibagi dengan
faktor 2:
Aplikasi Digital
Konversi Desimal ke Biner
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Metode
Sum-of-Weight.
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Pengulangan
pembagian dengan Metode bilangan 2.
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Konversi
fraksi desimal ke biner.
*Metode Sum-of-Weight
Bilangan desimal 9
sebagai The decimal number 9, for example, can be expressed as the sum of
binary weight of:
Convert the
following decimal numbers to binary:
a) 12 = 1100
b) 25 = 11001
c) 58 = 111010
d) 82 = 1010010
*Repeated Division by 2 Method
*Converting Decimal Fractions to Binary
l Addition, Subtraction, Multiplication, and Division
Binary Addition
Binary Subtraction
Binary 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
Binary Division
Division in
binary follows the same procedure as division in decimal.
1’s and 2’s Complements of
Binary Numbers
l The 1’s and 2’s Complements of
Binary Numbers are very important because they permit the representation of
negative numbers.
l The method of 2’s compliment
arithmetic is commonly used in computers to handle negative numbers
The 1’s
complement of a binary number is found by changing all 1s to 0s and all 0s to
1s.
Example:
1 0 1 1 0 0 1
0 (Binary Number)
The 2’s
complement of a binary number is found by adding 1 to the LSB of the 1’s
complement
2's Complement = (1's Complement) + 1
Example :
Alternative Method to find 2’s Complement
l
Start at
the right with the LSB and write the bits as they are up and including the
first 1
l
Take the
1’s complements of the remaining bits
Digital systems,
such as the computer, must be able to handle both positive and negative
numbers. A signed binary number consists of both sign and magnitude
information. The sign indicates whether a number is positive or negative and
the magnitude is the value of the number. There three forms in which signed
integer (whole) numbers can be represented in binary:
- Sign-Magnitude
- 1’s Complement
- 2’s Complement
Example :
Express the decimal number -39 in sign-magnitude, 1’s complement and
2’s complement,
-39 = 00100111
*Sign-Magnitude:
Decimal Value of positive and negative numbers in the sign-magnitude form are determined by summing the weights in all the magnitude bit positions where there are 1s and ignoring those positions where there are zeros.
*1’s Complement :
Decimal values of negative numbers are determined by assigning a
negative value to the weight of the sign bit, summing all the weight where
there are 1s and adding 1 to the result
Arithmetic Operations with Signed Number
In this section we will learn how signed numbers are added, subtracted,
multiplied and divided. This section will cover only on the 2’s complement
arithmetic, because, it widely used in computers and microprocessor-based
system .
· *Subtraction
· *Multiplication
· *Division
Hexadecimal Numbers :
l
Most
digital systems deal with groups of bits in even powers of 2 such as 8, 16, 32,
and 64 bits.
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Hexadecimal
uses groups of 4 bits.
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Base 16
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16
possible symbols
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0-9 and
A-F
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Allows
for convenient handling of long binary strings.
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Hexadecimal
is useful for representing long strings of bits.
l
Understanding
the conversion process and memorizing the 4 bit patterns for each hexadecimal
digit will prove valuable later.
BCD
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Binary
Coded Decimal (BCD) is another way to present decimal numbers in binary form.
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BCD is
widely used and combines features of both decimal and binary systems.
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Each
digit is converted to a binary equivalent.
8 7 4
1000
0111 0100 =
100001110100BCD
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Each
decimal digit is represented using 4 bits.
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Each
4-bit group can never be greater than 9.
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Reverse
the process to convert BCD to decimal.
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BCD is a
decimal number with each digit encoded to its binary equivalent.
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A BCD
number is not the same as a straight binary number.
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The
primary advantage of BCD is the relative ease of converting to and from
decimal.
Alphanumeric Codes
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Represents
characters and functions found on a computer keyboard.
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ASCII –
American Standard Code for Information Interchange.
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Seven
bit code: 27 = 128 possible code groups
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Table
2-4 lists the standard ASCII codes
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Examples
of use are: to transfer information
between computers, between computers and printers, and for internal storage.
NIM : 2003015077
Mata Kuliah : Sistem Digital dan Gelombang
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Sumber: https://onlinelearning.uhamka.ac.id
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