Day 12

 Hallo every body today I will speak with you about anew transformation

like: from Binary to Octal and vice versa

:For Example*

Transfer (11101011) from Binary to Octal

Binary System

The binary numeral system uses the number 2 as its base (radix). As a base-2 numeral system, it consists of only two numbers: 0 and 1. 

While it has been applied in ancient Egypt, China and India for different purposes, the binary system has become the language of electronics and computers in the modern world. This is the most efficient system to detect an electric signal’s off (0) and on (1) state. It is also the basis for binary code that is used to compose data in computer-based machines. Even the digital text that you are reading right now consists of binary numbers.

Reading a binary number is easier than it looks: This is a positional system; therefore, every digit in a binary number is raised to the powers of 2, starting from the rightmost with 2⁰. In the binary system, each binary digit refers to 1 bit.

The Octal System

The octal number system (or shortly oct) uses the number 8 as its base (radix). As a base-8 numeral system, it uses eight symbols: The numbers from 0 to 7, namely 0, 1, 2, 3, 4, 5, 6 and 7. Although it was used by some native American tribes until the 20th century, the octal system has become popular in the early ages of computing as a language of computer programming. This is because the octal system shortens binary by simplifying long and complex chains of binary displays used by computers.

The octal system is mainly used for counting binary in groups of three: Each octal digit represents three binary digits. Since 8 is 2 to the third power (2³), the octal system became a perfect abbreviation of binary for machines that employ word sizes divisible by three - which were 6-bit, 12-bit, 24-bit or 36-bit. Nowadays, most modern systems use hexadecimal rather than octal. However, octal numbers are an important part of basic knowledge in electronics.

How to Convert Binary to Octal

Converting from binary to octal is very easy since octal numbers are only simplified versions of binary strings. You just need to remember that each octal digit represents three binary digits so that three binary digits will give only one octal digit. While the method is quite easier than it sounds, it’s always useful to use a binary to octal conversion chart to save time.

• Step 1: Write down the binary number and group the 0’s and 1’s in sets of three. Start doing this from the right. If the leftmost group doesn’t have enough digits to make up a set of three, add extra 0’s to make another group.
• Step 2: Write 4, 2 and 1 below each group. These are the weights that the positions carry (2²,2¹,2⁰).
• Step 3: Every group of three in binary will give you one digit in octal. Multiply the 4, 2 and 1’s by the digit above.
• Step 4: Add the products within each set of three. Write the sums below the groups they belong to.
• Step 5: The digits you get from the sums in each group will give you the octal number, from left to right.