Tugas 3 Bravo Sistem Bilangan
Nama: Bravo
Marvel
Kelas: 2B
Nim:
2103015233
Rangkuman Sistem Bilangan
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
l Desimal > 0 ~ 9
l Biner > 0 ~ 1
l Oktal > 0 ~ 7
l Hexadesimal > 0 ~ F
Bilangan
Biner
l Sistem Bilangan biner merupakan cara
lain untuk melambangkan kuantitas, dimana 1 (HIGH) dan 0 (LOW).
l Sistem bilangan biner mempunyai nilai
basis 2 dengan nilai setiap posisi dibagi dengan faktor 2
Contoh :
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
l Metode Sum-of-Weight.
l Pengulangan pembagian dengan Metode
bilangan 2.
l Konversi fraksi desimal ke biner.
Binary
Arithmetic
l Binary arithmetic is essential in all
digital computers and in many other types of digital systems.
l Addition, Subtraction,
Multiplication, and Division
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
Signed
Numbers
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:
1.
Sign-Magnitude
2.
1’s
Complement
3.
2’s
Complement
1’s
Complement Form
Positive
numbers in 1’s complement form are represented the same way as the positive
sign-magnitude numbers. Negative numbers, however, are the 1’s complements of
the corresponding positive numbers. Example: The decimal number -25 is
expressed as the 1’s complement of +25 (00011001) as (11100110)
2’s
Complement Form
In the 2’s
complement form, a negative number is the 2’s complement of the corresponding
positive number
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 .
Hexadecimal
Numbers
l Most digital systems deal with groups
of bits in even powers of 2 such as 8, 16, 32, and 64 bits.
l Hexadecimal uses groups of 4 bits.
l Base 16
l 16 possible symbols
l 0-9 and A-F
l Allows for convenient handling of
long binary strings.
Hexadecimal
Numbers
l Convert from decimal to hex by using
the repeated division method used for decimal to binary and decimal to octal
conversion.
l Divide the decimal number by 16
l The first remainder is the LSB and
the last is the MSB.
l Note, when done on a calculator a
decimal remainder can be multiplied by 16 to get the result. If the remainder is greater than 9, the
letters A through F are used.
BCD
l Binary Coded Decimal (BCD) is another
way to present decimal numbers in binary form.
l BCD is widely used and combines
features of both decimal and binary systems.
l Each digit is converted to a binary
equivalent.
Alphanumeric
Codes
l Represents characters and functions
found on a computer keyboard.
l ASCII – American Standard Code for
Information Interchange.
l Seven bit code: 27 = 128
possible code groups
l Table 2-4 lists the standard ASCII
codes
l Examples of use are: to transfer information between computers,
between computers and printers, and for internal storage
Soal-Soal
1. Konversikan
bilangan oktal 64 menjadi bentuk biner
A. 6
B.
3
C.
1
D.
8
Jawaban: A
2. Ubah bilangan
biner (2) berikut ini menjadi bilangan
1010001(2) =
….. (10)
A.23(10)
B.81(10)
C.77(10)
D.51(10)
Jawaban: B
3. Diketahui −3≤n<2, jika n anggota
himpunan bilangan bulat, maka himpunan penyelesaiannya adalah
A.{-3, -2, -1, 0 ,1}
B.{-3, 0, 1, 2 ,3}
C.{-2, -1, 0 ,1 ,4}
D.{-5, -6, 0 ,1 ,3}
Jawaban: A
4. Diketahui A∗B=(A+B)2−3AB, Maka nilai
dari 2∗4=
A.3
B.9
C.12
D.4
Jawaban= C
5. Konversikan bilangan desimal ke
biner: 1. 137
A.22201121
B. 10001001
C. 21100001
D.10011001
Jawaban: B
6. Konversikan bilangan desimal ke
biner: 212
A.11011111
B. 11090002
C. 10001001
D. 11010100
Jawaban: D
7. Konversikan bilangan desimal nilai 50
menjadi bilangan biner:
A. 1100102
B. 2212990
C.1000112
D.1100221
Jawaban: A
8. konversi bilangan oktal 145 ke
bilangan hexadecimal
A. 201^1
B. 111^2
C. 101^10
D. 200^1
Jawaban: C
9. Cara menentukan bagaimana suatu
bilangan dapat diwakili menggunakan simbol yang telah disepakati (standar)
adalah pengertian umum dari___
A.Sistem Nasional
B.Sistem penilaian
C.Sistem Pengukuran
D.Sistem Bilangan
Jawaban: E
10.Cara menentukan bagaimana suatu
bilangan dapat diwakili menggunakan simbol yang telah disepakati (standar)
adalah pengertian umum dari___
A.Sistem Nasional
B.Sistem penilaian
C.Sistem Pengukuran
D.Sistem Internasional
Jawaban: A
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