Binary Number System
Binary and IPv4 Addresses
- Binary numbering system consists of 1s and 0s, called bits
- Decimal numbering system consists of digits 0 through 9
- Hosts, servers, and network equipment using binary addressing to identify each other.
- Each address is made up of a string of 32 bits, divided into four sections called octets.
- Each octet contains 8 bits (or 1 byte) separated by a dot.
- For ease of use by people, this dotted notation is converted to dotted decimal.
Video - Converting Between Binary and Decimal Numbering Systems
Binary Positional Notation
Positional notation means that a digit represents different values depending on the “position” the digit occupies in the sequence of numbers.
The decimal positional notation system operates as described in the table. Radix | 10 | 10 | 10 | 10 — | — | — | — | — Position in Number | 3 | 2 | 1 | 0 Calculate | (10^3) | (10^2) | (10^1) | (10^0) Position value | 1000 | 100 | 10 | 1
The binary positional notation system operates as shown in the tables below. Radix | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 — | — | — | — | — | — | — | — | — Position in Number | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 Calculate | (2^7) | (2^6) | (2^5) | (2^4) | (2^3) | (2^2) | (2^1) | (2^0) Position value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1
IPv4 Addresses
Routers and computers only understand binary, while humans work in decimal. It is important for you to gain a thorough understanding of these two numbering systems and how they are used in networking.
Hexadecimal Number System
Hexadecimal and IPv6 Addresses
- To understand IPv6 addresses, you must be able to convert hexadecimal to decimal and vice versa.
- Hexadecimal is a base sixteen numbering system, using the digits 0 through 9 and letters A to F.
- It is easier to express a value as a single hexadecimal digit than as four binary bit.
- Hexadecimal is used to represent IPv6 addresses and MAC addresses.
- IPv6 addresses are 128 bits in length. Every 4 bits is represented by a single hexadecimal digit. That makes the IPv6 address a total of 32 hexadecimal values.
- The figure shows the preferred method of writing out an IPv6 address, with each X representing four hexadecimal values.
- Each four hexadecimal character group is referred to as a hextet.
Decimal to Hexadecimal Conversions
Follow the steps listed to convert decimal numbers to hexadecimal values:
- Convert the decimal number to 8-bit binary strings.
- Divide the binary strings in groups of four starting from the rightmost position.
- Convert each four binary numbers into their equivalent hexadecimal digit.
For example, 168 converted into hex using the three-step process.
- 168 in binary is 10101000.
- 10101000 in two groups of four binary digits is 1010 and 1000.
- 1010 is hex A and 1000 is hex 8, so 168 is A8 in hexadecimal.
Hexadecimal to Decimal Conversion
Follow the steps listed to convert hexadecimal numbers to decimal values:
- Convert the hexadecimal number to 4-bit binary strings.
- Create 8-bit binary grouping starting from the rightmost position.
- Convert each 8-bit binary grouping into their equivalent decimal digit.
For example, D2 converted into decimal using the three-step process:
- D2 in 4-bit binary strings is 1101 and 0010.
- 1101 and 0010 is 11010010 in an 8-bit grouping.
- 11010010 in binary is equivalent to 210 in decimal, so D2 is 210 is decimal