Substance:
- BINARY NUMBER SYSTEM
- OCTAL NUMBER SYSTEM / OCTAL
- DECIMAL NUMBER SYSTEM / DECIMAL
- HEXADECIMAL NUMBER SYSTEM / HEXADESIMAL
- BINARY, OCTAL, DECIMAL/DECIMAL, AND HEXADECIMAL/HEXADESIMAL NUMBER CONVERSION
- BINARY to DECIMAL Conversion Example
- Example of DECIMAL to BINARY Conversion
- OCTAL to DECIMAL Conversion
- OCTAL/OCTAL to BINARY Conversion Example
- Convert DECIMAL to OCTAL
- Example of HEXADECIMAL / HEXADESIMAL to DECIMAL / DECIMAL Conversion
- Example of TRUTH TABLE OF NUMBER SYSTEM.
- SMK Version Notes
1. Binary Number System
Radix (Basis) = 2 {0,1}A binary number can be written or marked with the number (2) below it, an example of how to write it is as below:
1011(2)Information:
2. Octal Number System
Radix (Basis) = 8 {0,1,2,3,4,5,6,7}A binary number can be written or marked with the number (8) below it, an example of how to write it is as below:
20 (8)3. Decimal Number System
Radix (Basis) = 10 {0,1,2,3,4,5,6,7,8,9}A decimal number can be written or marked with the number (10) below it, an example of how to write it is as below:
7225,25(10)4. Hexadecimal Number System
Comes from the word HEXA which means 6 and DECEM which means 10, so HEXADECIMAL has
Radix (Basis) = 16 {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}A decimal number can be written or marked with the number (16) below it, an example of how to write it is as below:
7225,25(16)5. Binary, Octal, Decimal & Hexadecial Number Conversion
Previously, to make it easier to understand the process of converting a number, first pay attention to the truth of Decimal as follows, by converting DECIMAL TO DECIMAL numbers as follows:
6. Convert BINARY to DECIMAL
7. Convert DECIMAL to BINARY
If the decimal number is a fractional value, then the way to convert it is by extracting (separating the integer from the fractional number) and the way to convert it is also different, if the integer is divided by 2, while the fractional number is multiplied by 2, for more details please see the following example 3:
8. Convert OCTAL to DECIMAL
9. Convert DECIMAL to OCTAL
10. Convert OCTAL to BINARY
The steps to convert from OCTAL to BINARY must go through DECIMAL first, illustration OCTAL --> DECIMAL --> BINARY.
11. Convert HEXADECIMAL to DECIMAL
12. Truth Table of Number System
| DECIMAL | BINER | OCTAL | HEXADECIMAL |
|---------|-------|-------|-------------|
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 17 | 10001 | 21 | 11 |
| 18 | 10010 | 22 | 12 |
| 19 | 10011 | 23 | 13 |
| 20 | 10100 | 24 | 14 |13. SMK Version Notes
| SMKN 2 YOGYAKARTA | Kompetensi | Kode : 04/PDTM/KL-XII/1 |
|-----------------------------------|-----------------|------------------------------------|
| Prog. Keahlian : Tek. Audio Video | SISTEM BILANGAN | Waktu : menit |
| Prog. Diklat : PDTM | | Nama Siswa : |
| Kelas : XII AV | | Tanggal : |In general, there are 4 types of number systems used, namely:
- Decimal Number System (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
- Binary Number System (0, 1)
- Hexadecimal Number System (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F)
- Octal Number System (0, 1, 2, 3, 4, 5, 6, 7)
These four number systems are distinguished from each other by a value called "Base" or "Radix". The Decimal number system uses base 10, Binary numbers use base 2, Hexadecimal numbers use base 16 and Octal numbers use base 8.
1. Number Conversion
A number can be expressed in 4 different presentations of numbers or symbols. To get the value of a number or the equivalent of a number in one base to another, the number conversion method is used.
a. Converting Decimal Numbers to Binary
There are two techniques for converting decimal numbers to binary numbers, namely:
- technique for
- less technique
- technique gives logic 1 according to its value.
1. Convert decimal numbers to binary using the division technique
2. Convert decimal numbers to binary using the subtraction technique
3. Convert decimal numbers to binary using the technique of giving logic-1 according to their value.
b. Converting Decimal Numbers to Hexadecimal
44 10 = ................. 16 (using the technique of dividing by 16) 44 : 16 = 2 remainder 12
12 = C
So 44 10 = 2C 16
c. Converting Binary Numbers to Hexadecimal
Gives logic 1 according to the bit level
Gives logic 1 according to the bit level
Logic 1 in MSB has a value of 2, logic 1 in LSB has a value of (4 + 8 = 12) 12 is the same as C in Hexadecimal numbers.
d. Converting Hexadecimal Numbers to Binary
Gives logic 1 at the bit level
Give logic 1 according to the bit level!
Task: Convert the numbers below
There are several number systems used in digital systems. The most common are decimal, binary, octal, and hexadecimal number systems. The decimal number system is the number system that is most familiar to us because of its various conveniences that we use every day. The binary number system is the number system that is most widely used in digital systems because this number system can directly represent existing logic. Meanwhile, the octal and hexadecimal number systems are usually widely used in digital systems to shorten the presentation of a number that was previously presented in the binary number system.
In general, numbers can be divided into several categories. In terms of decimal points (points), numbers can be divided into integer numbers (fixed-point numbers) and fractional numbers (floating-point numbers). And in terms of signs, numbers can be divided into unsigned numbers and signed numbers. This chapter will explain unsigned integers, signed integers and unsigned fractional numbers (floating-point numbers). By studying some of the characteristics of a number system.
2. Decimal
The decimal number system is composed of 10 numbers or symbols. By using these symbols as digits in a number, we can express a quantity. The ten symbols are:
D = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
The decimal number system is also called the base 10 or radix 10 number system because it has 10 digits. This number system is natural because in reality humans have 10 fingers. The word digit itself is derived from the Latin word finger.
The characteristic of a number using the decimal number system is the addition of the subscript dec or 10 or the addition of D at the end of a number. Example: 357des = 35710 = 357D. However, because decimal numbers have become numbers used everyday, the subscript is usually omitted.
The decimal number system is a positional-value system. In this system, the value of a digit depends on its position. The representation of an integer decimal number of m digits is as follows,
So an m digit decimal number will have the value:
Example:
Number 357
In that number, the digit 3 means 3 hundreds, 5 means 5 tens, and 7 means 7 units. So, 3 has the greatest meaning among the three digits. This digit acts as the most significant digit (Most Significant Digit, MSD). While 7 has the smallest meaning among the three digits and is called the least significant digit (Least Significant Digit, LSD).
For fractional decimal numbers, the value representation is as follows,
So a fractional decimal number will have the value:
The decimal point is used to separate the integer and fractional parts of a number. Its position relative to the decimal point gives it a meaning that can be expressed as a power of 10.
Example:
The number 35.27.
This number means 3 tens plus 5 ones plus 2 tens plus 7 hundredths. The decimal point separates the positive exponents of 10 from the negative exponents.
In general, it can be said that the value of a decimal number is the sum of the multiplication of each digit by its position value.
3. Binary
Digital systems only recognize two logics, namely 0 and 1. Logic 0 usually represents the off condition and logic 1 represents the on condition. In the binary number system, only two symbols are known, namely 0 and 1. Therefore, the binary number system is most often used to represent quantities and represent states in digital systems and computer systems.
A binary digit is called a binary digit or bit. Four bits are called a nibble and eight bits are called a byte. A number of bits that a computer can process to represent a character (which can be a letter, number or special symbol) is called a word. A computer can process one word of data consisting of 4 to 64 bits. For example, a computer using a 32-bit microprocessor can receive, process, store and send data or instructions in 32-bit format.
If the computer is used to process characters, then the characters (including letters, numbers, punctuation marks and control characters) must be formatted in the form of alphanumeric codes. The standard ASCII (American Standard Code for Information Interchange) format uses a seven-bit data format to represent all existing characters including punctuation marks and control markers. With a seven-bit format, ASCII can accommodate 27 = 128 data.
The binary number system is a base two number system. In this number system, only two symbols are known, namely:
The characteristic of a number using the binary number system is the addition of the subscript bin or 2 or the addition of the letter B at the end of a number. Example:
The representation of an m bit integer binary number is as follows,
So a binary number m bits will have the value:
The leftmost bit of a binary number acts as the most significant bit (MSB), while the rightmost bit acts as the least significant bit (LSB).
For fractional binary numbers, the value representation is as follows,
So a fractional binary number will have the value:
This equation can be used to convert a binary number to a decimal number.
a) Converting Binary Numbers to Decimal
Converting a binary number to decimal is done by adding the results of multiplying all the binary bits by their weights. Example:
Converting Binary Numbers to Decimal
b) Converting Decimal Numbers to Binary
Converting whole decimal numbers to binary is done by repeatedly dividing a decimal number by 2. The remainder of each division is the bit obtained. Example:
Converting Whole Decimal Numbers to Binary
Netizens
Q1:
- EKO SYAHPUTRA 13 Nov 2015, 20:40:00 useful for us beginners, bro.. (y)
- JOSSUUUU Dec 8, 2015, 23:24:00 bro, why is your octal to binary conversion different from other blogs?
- AGSAL FAP 19 Jan 2016, 17:43:00 Very useful blog, bro, for preparing for class 12 physics
- ARSHA MUHAMMAD Nov 26, 2016, 16:38:00 Thank you, sis, the material in this blog is useful.
A1:
- Hello Eko S, Thank you, thank you very much, glad to hear that, good luck
- My review explains using rules, while in the blog you are referring to it explains based on clouds.
- The picture is like both explaining 3 to the power of 3, if I use the rule, namely 3x3x3 = 27 if the blog is 3 to the power of 3 = 27 (directly)
- Okay, for the purpose of solving the problem both are correct, but if to explain to the younger siblings who are still newbies? (I think they need enlightenment on how the process works) while on the blog I think it is more suitable for those who already understand and are familiar with the digital system before, so they can still be invited to use the cloud method, that's it, bro, thank you..
- Hello AGSAL FAP Thank you, glad to hear that, okay then, happy studying and always be successful
- Hello ARSHA MUHAMMAD, you're welcome, amen, thank goodness for that