Binary Numbers are represented by a series of binary digits which increase in powers of 2 from right to left
In this binary numbers tutorial we will see that binary digits called bits are written in base-2 so need two digits, zero and one. That is the binary numbering system we represent words and numbers using only the two digits 0 and 1.
There are different yet similar types of binary numbering systems used in digital electronic circuits and computers. However, the numbering system used in one type of circuit may be different to that of another type of circuit, for example, the memory of a computer would use hexadecimal numbers while the keyboard uses decimal numbers.
Then the conversion from one number system to another is very important with the four main forms of arithmetic being.
Long binary numbers are difficult to both read or write and are generally converted into a system more easily understood or user friendly. The two most common derivatives based on binary numbers are the Octal and the Hexadecimal numbering systems, with both of these limited in length to a byte (8-bits) or a word (16-bits).
Octal numbers can be represented by groups of 3-bits and hexadecimal numbers by groups of 4-bits together, with this grouping of the bits being used in electronic or computer systems in displays or printouts. The grouping together of binary numbers can also be used to represent Machine Code used for programming instructions and control such as an Assembly Language.
Comparisons between the various Decimal, Binary, Hexadecimal and Octal numbers are given in the following table.
Base, b | Byte (8-bits) | Word (16-bits) |
Decimal | 0 to 25510 |
0 to 65,53510 |
Binary | 0000 0000 to 1111 11112 |
0000 0000 0000 0000 to 1111 1111 1111 11112 |
Hexadecimal | 00 to FF16 |
0000 to FFFF16 |
Octal | 000 to 3778 |
000 000 to 177 7778 |
We can see from the table above in this binary numbers tutorial that the Hexadecimal numbering system uses only four digits to express a single 16-bit word length, and as a result it is the most commonly used Base Numbering System for digital, micro-electronic and computer systems.
Please provide notes
Very interesting
Thank you for your best proposal of computer science.
I want to know how to convert binary code to decimals
How to draw Binary number 110 by 10 in binary form
I am not a beginner but a consultant engineer (I work in Italy) who often does seminars in electroacoustics. Yours is a great job, I congratulate you.
Thanks for all your tutorials.
Best regards
Gennaro Granito
Very informative site.
please give me some notes ..to gain knowledge.
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This give me some knowledge
The tutorials are wonderful and great, thank you so much on these on the AND gate how I wish I could see more circuits on these other gates as well as boolean algebra
Thanks so much about these notes about how to convert and I wish I would see some more examples of how to concert Binary to Decimal, Octadecimal.
thanks!!
converting binary number to decimal and show calculations
11101110011
1000101
Did you tell about binary?
11101110011
Starting at left, it’s 1-3-7-14-29-59-119-238-476-953-1907
So, 1907 is the decimal equivalent of the binary 11101110011
Good notes for beginners.