2101-Ch05.docx

IPv4 addresses begin as binary, a series of only 1s and 0s. These are difficult to manage, so network administrators must convert them to decimal. This topic shows you a few ways to do this. Binary is a numbering system that consists of the digits 0 and 1 called bits. In contrast, the decimal numbe...

IPv4 addresses begin as binary, a series of only 1s and 0s. These are difficult to manage, so network administrators must convert them to decimal. This topic shows you a few ways to do this. Binary is a numbering system that consists of the digits 0 and 1 called bits. In contrast, the decimal numbering system consists of 10 digits consisting of the digits 0 - 9. Binary is important for us to understand because hosts, servers, and network devices use binary addressing. Specifically, they use binary IPv4 addresses, as shown in the figure, to identify each other. Each address consists of a string of 32 bits, divided into four sections called octets. Each octet contains 8 bits (or 1 byte) separated with a dot. For example, PC1 in the figure is assigned IPv4 address 11000000.10101000.00001010.00001010. Its default gateway address would be that of R1 Gigabit Ethernet interface 11000000.10101000.00001010.00000001. Binary works well with hosts and network devices. However, it is very challenging for humans to work with. For ease of use by people, IPv4 addresses are commonly expressed in dotted decimal notation For a solid understanding of network addressing, it is necessary to know binary addressing and gain practical skills converting between binary and dotted decimal IPv4 addresses. This section will cover how to convert between base two (binary) and base 10 (decimal) numbering systems. Learning to convert binary to decimal requires an understanding of positional notation. Positional notation means that a digit represents different values depending on the "position" the digit occupies in the sequence of numbers. You already know the most common numbering system, the decimal (base 10) notation system. To help understand the process, consider the IP address **192.168.10.11**. The first octet number **192** is converted to binary using the previously explained positional notation process. It is possible to bypass the process of subtraction with easier or smaller decimal numbers. For instance, notice that it is fairly easy to calculate the third octet converted to a binary number without actually going through the subtraction process (8 + 2 = 10). The binary value of the third octet is **00001010**. The fourth octet is 11 (8 + 2 + 1). The binary value of the fourth octet is **00001011**. Converting between binary and decimal may seem challenging at first, but with practice it should become easier over time. Binary and hexadecimal work well together because it is easier to express a value as a single hexadecimal digit than as four binary bits. The hexadecimal numbering system is used in networking to represent IP Version 6 addresses and Ethernet MAC addresses. IPv6 addresses are 128 bits in length and every 4 bits is represented by a single hexadecimal digit; for a total of 32 hexadecimal values. IPv6 addresses are not case-sensitive and can be written in either lowercase or uppercase. the preferred format for writing an IPv6 address is x:x:x:x:x:x:x:x, with each "x" consisting of four hexadecimal values. When referring to 8 bits of an IPv4 address we use the term octet. In IPv6, a *hextet* is the unofficial term used to refer to a segment of 16 bits or four hexadecimal values. Each "x" is a single hextet, 16 bits, or four hexadecimal digits. Converting decimal numbers to hexadecimal values is straightforward. Follow the steps listed: 1. Convert the decimal number to 8-bit binary strings. 2. Divide the binary strings in groups of four starting from the rightmost position. 3. Convert each four binary numbers into their equivalent hexadecimal digit. The example provides the steps for converting **168** to hexadecimal. For example, **168** converted into hex using the three-step process. 1. **168** in binary is **10101000**. 2. **10101000** in two groups of four binary digits is **1010** and **1000**. 3. **1010**is hex **A** and **1000** is hex **8**. **Answer:** **168** is **A8** in hexadecimal. Converting hexadecimal numbers to decimal values is also straightforward. Follow the steps listed: 1. Convert the hexadecimal number to 4-bit binary strings. 2. Create 8-bit binary grouping starting from the rightmost position. 3. Convert each 8-bit binary grouping into their equivalent decimal digit. This example provides the steps for converting **D2** to decimal. 1. **D2** in 4-bit binary strings is **1101** and **0010**. 2. **1101** and **0010** is **11010010** in an 8-bit grouping. 3. **11010010** in binary is equivalent to **210** in decimal. **Answer:** **D2** in hexadecimal is **210** in decimal. Decimal to Binary facts 1. **IPv4 Address Structure**: An IPv4 address is a 32-bit number divided into four 8-bit groups called octets. [Each octet is separated by a dot in the decimal format (e.g., 192.168.1.1) and can be converted individually into binary^1^](https://whatismyipaddress.com/ip-address-to-binary). 2. **Binary Representation**: In binary, each octet is represented by 8 bits. [For example, the decimal number 192 converts to the binary number 11000000^2^](https://www.networkacademy.io/ccna/ip-subnetting/converting-ip-addresses-into-binary). 3. **Subnetting and Routing**: Converting IPv4 addresses to binary is crucial for subnetting and routing. [It helps in understanding the network and host portions of the address, which is essential for network configuration and troubleshooting^1^](https://whatismyipaddress.com/ip-address-to-binary). 4. **Positional Notation**: The binary system uses positional notation, where each bit represents a power of two. [For instance, the rightmost bit represents (2\^0), the next bit represents (2\^1), and so on^2^](https://www.networkacademy.io/ccna/ip-subnetting/converting-ip-addresses-into-binary). 5. **Ease of Calculation**: While humans find decimal notation easier to read, computers and network devices operate using binary. [Converting to binary simplifies calculations for tasks like subnetting and determining network ranges^1^](https://whatismyipaddress.com/ip-address-to-binary). IPv6 Hexadecimal facts 1. **Length and Structure**: An IPv6 address is 128 bits long and is represented as eight groups of four hexadecimal digits, separated by colons. [Each group represents 16 bits^1^](https://www.ciscopress.com/articles/article.asp?p=2803866)[^2^](https://networkustad.com/2019/07/05/ipv6-address-representation/). 2. [**Hexadecimal Digits**: The address uses hexadecimal digits (0-9 and a-f), which can be written in either lowercase or uppercase^2^](https://networkustad.com/2019/07/05/ipv6-address-representation/). 3. [**Hextets**: Each group of four hexadecimal digits is informally called a "hextet," similar to the term "octet" used in IPv4 addressing^1^](https://www.ciscopress.com/articles/article.asp?p=2803866). 4. **Zero Compression**: IPv6 addresses can be shortened using zero compression. [Consecutive sections of zeros can be replaced with a double colon (::), but this can only be done once in an address](https://www.techrepublic.com/article/breaking-down-an-ipv6-address-what-it-all-means/) Top of Form Bottom of Form **Binary Number System** Binary is a numbering system that consists of the numbers 0 and 1 called bits. In contrast, the decimal numbering system consists of 10 digits consisting of the numbers 0 - 9. Binary is important for us to understand because hosts, servers, and network devices use binary addressing, specifically, binary IPv4 addresses, to identify each other. You must know binary addressing and how to convert between binary and dotted decimal IPv4 addresses. This topic presented a few ways to convert decimal to binary and binary to decimal. **Hexadecimal Number System** Just as decimal is a base ten number system, hexadecimal is a base sixteen system. The base sixteen number system uses the numbers 0 to 9 and the letters A to F. The hexadecimal numbering system is used in networking to represent IPv6 addresses and Ethernet MAC addresses. IPv6 addresses are 128 bits in length and every 4 bits is represented by a single hexadecimal digit; for a total of 32 hexadecimal values. To convert hexadecimal to decimal, you must first convert the hexadecimal to binary, then convert the binary to decimal. To convert decimal to hexadecimal, you must also first convert the decimal to binary.