Number systems and Conversion

Binary and hexadecimal numbers are a complete mystery for many of us. Often we don't find it really interesting because on the internet there are plenty of "subnet" or "binary" calculators where you can easily calculate from decimal to binary to hexadecimal or the other way around, without knowing how the exact calculation works.
This is no problem when you are not configuring or designing networks on a daily basis, but it will be a problem as soon as you take a networking examn, so it's best to know how to do these calculations off the top of your head.
Another advantage you will have is once you have mastered the art of binary calculations you can immediately see how big a network is and what the subnet mask is when people start throwing numbers at you.
So, let's start:

1. Decimal and Binary Numbers
When we write decimal (base 10) numbers, we use a positional notation system. Each digit is multiplied by an appropriate power of 10 depending on its position in the number:
For example:

843 = 8*10^2 + 4*10^1 + 3*10^0 = 8*100 + 4*10 + 3*1 = 800 + 40 + 3 = 843

For whole numbers, the rightmost digit position is the one's position (10^0 = 1). The numeral in that position indicates how many ones are present in the number. The next position to the left is ten's, then hundred's, thousand's, and so on. Each digit position has a weight that is ten times weight of the position to its right.
In the decimal number system, there are ten possible values that can appear in each digit position, and so there are ten numerals required to represent the quantity in each digit position. The decimal numerals are the familiar zero through nine (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
In a positional notation system, the number base is called the radix. Thus, the base ten system that we normally use has a radix of 10. The term radix and base can be used interchangeably. When writing numbers in a radix other than ten, or where the radix isn't clear from the context, it is customary to specify the radix using a subscript. Thus, in a case where the radix isn't understood, decimal numbers would be written like this:

Generally, the radix will be understood from the context and the radix specification is left off.

The binary number system is also a positional notation numbering system, but in this case, the base is not ten, but is instead two. Each digit position in a binary number represents a power of two. So, when we write a binary number, each binary digit is multiplied by an appropriate power of 2 based on the position in the number:
For example:

101101 = 1*2^5 + 0*2^4 + 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 1*32 + 0*16 + 1*8 + 1*4 + 0*2 + 1*1 = 32 + 8 + 4 + 1 = 45

In the binary number system, there are only two possible values that can appear in each digit position rather than the ten that can appear in a decimal number. Only the numerals 0 and 1 are used in binary numbers. The term "bit" is a contraction of the words "binary" and "digit", and when talking about binary numbers the terms bit and digit can be used interchangeably. When talking about binary numbers, it is often necessary to talk of the number of bits used to store or represent the number. This merely describes the number of binary digits that would be required to write the number. The number in the above example is a 6 bit number.
The following are some additional examples of binary numbers:

2. Conversion between Decimal and Binary
Converting a number from binary to decimal is quite easy. All that is required is to find the decimal value of each binary digit position containing a 1 and add them up.

The method for converting a decimal number to binary is one that can be used to convert from decimal to any number base. It involves successive division by the radix until the dividend reaches 0. At each division, the remainder provides a digit of the converted number, starting with the least significant digit.

3. Hexadecimal Numbers
In addition to binary, another number base that is commonly used in digital systems is base 16. This number system is called hexadecimal, and each digit position represents a power of 16. For any number base greater than ten, a problem occurs because there are more than ten symbols needed to represent the numerals for that number base. It is customary in these cases to use the ten decimal numerals followed by the letters of the alphabet beginning with A to provide the needed numerals. Since the hexadecimal system is base 16, there are sixteen numerals required. The following are the hexadecimal numerals:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

The reason for the common use of hexadecimal numbers is the relationship between the numbers 2 and 16. Sixteen is a power for 2 (16 = 2^4). Because of this relationshipp, four digits in a binary number can be represented with a single hexadecimal digit. This makes conversion between binary and hexadecimal numbers very easy, and hexadecimal can be used to write large binary numbers with much fewer digits. When working with large digital systems such as computers, it is common to find binary numbers with 8, 16 and even 32 digits. Writing a 16 or 32 bit binary number would be quite tedious and error prone. By using hexadecimal, the numbers can be written with fewer digits and much less likelihood of error.
To convert a binary number to hexadecimal, divide it into groups of four digits starting with the rightmost digit. If the number of digits isn't a multiple of 4, prefix the number with 0's so that each group contain 4 digits. For each four digit group, convert the 4 bit binary number into an equivalent hexadecimal digit.
There are several ways in common use to specify that a given number is in hexadecimal representation rather than some other radix. In cases where the context makes it absolutely clear that numbers are represented in hexadecimal, no indicator is used. In much wirtten material where the context doesn't make it clear what the radix is, the numeric subscript 16 following the hexadecimal number is used. In most programming languages, this method isn't really feasible, so there are several conventions used depending on the language. In the C and C++ languages, hexadecimal constants are represented with a "0x" preceding the number, as in: 0x317F, or 0x1234, or 0xAF. In assembler programming languages that follow the Intel style, a hexadecimal constant begins with a numeric character (so that the assembler can distinguish it from a variable name), a leading "0" being used if necessary. The letter "h" is then suffixed onto the number to inform the assembler that it is a hexadecimal constant. In Intel style assembler format: 371Fh and 0FABCh are valid hexadecimal constants.

4. Binary Coded Decimal Numbers
Another number system that is encountered occasionally is Binary Coded Decimal. In this system, numbers are represented in a decimal form, however each decimal digit is encoded using a four bit binary number.

136 = 0001 0011 0110

Conversion of numbers between decimal and BCD is quite simple. To convert from decimal to BCD, simply write down the four bit binary pattern for each decimal digit. To convert from BCD to decimal, divide the number into groups of 4 bits and write down the corresponding decimal digit for each 4 bit group.
There are a couple of variations on the BCD representation, namely packed and unpacked. An unpacked BCD number has only a single decimal digit stored in each data byte. In this case, the decimal digit will be in the low four bits and the upper 4 bits of the byte will be 0. In the packed BCD representation, two decimal digits are placed in each byte. Generally, the high order bits of the data byte contain the more significant decimal digit.
Example:

01010110 10010011
This is converted to a decimal number as follows:
0101 0110 1001 0011
 5     6   9     3

The use of BCD to represent numbers isn't as common as binary in most computer systems, as it is not as space efficient. In packed BCD, only 10 of the 16 possible bit patterns in each 4 bit unit are used. In unpacked BCD, only 10 of the 256 possible bit patterns in each byte are used. A 16 bit quantify can represent the range 0 - 65535 in binary, 0 - 9999 in packed BCD and only 0-99 in unpacked BCD.

5. Fixed Precision and Overflow
So far, in talking about binary numbers, we haven't considered the maximum size of the number. We have assumed that as many bits are available as needed to represent the number. In most computer systems, this isn't the case. Numbers in computers are typically represented using a fixed number of bits. These sizes are typically 8 bits, 16 bits, 32 bits, 64 bits and 80 bits. These sizes are generally a multiple of 8, as most computer memories are organized on an 8 bit byte basis. Numbers in which a specific number of bits are used to represent the value are called fixed precision numbers. When a specific number of bits are used to represent a number, that determines the range of possible values that can be represented. For example, there are 256 possible combinations of 8 bits, therefore an 8 bit number can represent 256 distinct numeric values and the range is typically considered to be 0-255. Any number larger than 255 can't be represented using 8 bits. Similarly, 16 bits allows a range of 0-65535.
When fixed precision numbers are used, the concept of overflow must be considered. An overflow occurs when the result of a calculation can't be represented with the number of bits available. For example when adding the two eight bit quantities: 150 + 170 = 320. This is outside the range 0-255, and so the result can't be represented using 8 bits. The result has overflowed the available range. When overflow occurs, the low order bits of the result will remain valid, but the high order bits will be lost. This result in a value that is significantly smaller than the correct result.

6. Signed and Unsigned Numbers
So far, we have only considered positive values for binary numbers. When a fixed precision binary number is used to hold only positive values, it is said to be unsigned. In this case, the range of positive values that can be represented is 0 --2^n - 1, where n is the number of bits used. It is also possible to represent signed (negative as well as positive) numbers in binary. In this case, part of the total range of values is used to represent positive values, and the rest of the range is used to represent negative values.
There are several ways that signed numbers can be represented in binary, but the most common representation used today is called two's complement. The term two's complement is somewhat ambiguous, in that it is used in two different ways. First, as a representation, two's complement is a way of interpreting and assigning meaning to a bit pattern contained in a fixed precision binary quantify. Second, the term two's complement is also used to refer to an operation that can be performed on the bits of a binary quantity. As an operation, the two's complement of a number is formed by inverting all of the bits and adding 1. In a binary number being interpreted using the two's complement representation, the high order bit of the number indicates the sign. If the sign bit is 0, the number is positive, and if the sign bit is 1, the number is negative. For positive numbers, the rest of the bits hold the true magnitude of the number. For negative numbers, the lower order bits hold the complement (or bitwise inverse) of the magnitude of the number. It is important to note that two's complement representation can only be applied to fixed precision quantities, that is, quantities where there are a set number of bits.
Two's complement representation is used because it reduces the complexity of hardware in the arithmetic-logic unit of a computer's CPU. Using two's complement representation, all of the arithmetic operations can be performed by the same hardware whether the numbers are considered to be unsigned or signed. The bit operations performed are identical, the difference comes from the interpretation of the bits. The interpretation of the value will be different depending on whether the value is considered to be unsigned or signed.

Example: Find the two's complement of the following 8 bit number: 00101001
 11010110 (first invert the bits)
+00000001 (then add 1)
=11010111

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Network Address Translation (NAT)

         This section explains Network Address Translation (NAT). NAT is also known as IP masquerading. It provides a mapping between internat IP addresses and officially assigned external addresses.
        Originally, NAT was suggested as a short-term solution to the problem of IP address depletion. Also, many organizations have, in the past, used locally assigned IP addresses, not expecting to require Internet connectivity.

        The idea of NAT is based on the fact that only a small number of the hosts in a private network are communicating outside of that network. If each host is assigned an IP address from the official IP address pool only when they need to communicate, then only a small number of official addresses are required.
        NAT might be a solution for networks that have private address ranges or unofficial addresses and want to communicate with hosts on the Internet. In fact, most of the time, this can also be achieved by implementing a firewall. Hence, clients that communicate with the Internet by using a proxy or SOCKS server do not expose their addresses to the Internet, so their addresses do not have to be translated anyway. However, for any reason, when proxy and SOCKS are not available, or do not meet specific requirements, NAT might be used to manage the traffic between the internal and external network without advertising the internal host addresses.
        Consider an internal network that is based on the private IP address space, and the users want to use an application protocol for which there is no application gateway; the only option is to estabilish IP-level connectivity between hosts in the internal network and hosts on the Internet. Since the routers in the Internet would not know how to route IP packets back to a private IP address, there is no point in sending IP packets with private IP addresses as source IP addresses through a router into the Internet.
        NAT takes the IP address of an outgoing packet and dynamically translates it to an officially assigned global address. For incoming packets it translates the assigned address to an internal address.

        From the point of two hosts that exchange IP packets with each other, one in the secure network and one in the non-secure network, NAT looks like a standard IP router that forwards IP packets between two network interfaces.

        For each outgoing IP packet, the source address is checked by the NAT configuration rules. If a rule matches the source address, the address is translated to a global address from the address pool. The predefined address pool contains the addresses that NAT can use for translation. For each incoming packet, the destination address is checked if it is used by NAT. When this is true, the address is translated to the original internal address.

         If NAT translates an address for an IP packet, the checksum is also adjusted. For FTP packets, the task is even more difficult, because the packets can contain addresses in the data of the packet. For example, the FTP PORT command contains an IP address in ASCII. These addresses should also be translated correctly and checksum updates and even TCP sequence and acknowledgement updates should be made accordingly.
        NAT looks like a normal IP router to the systems which use it. In order to make the routing tables work, the IP network design should choose addresses as if connecting two or more IP networks or subnets through a router. The NAT IP addresses need to come from separate networks or subnets, and the addresses need to be unambiguous with respect to other networks or subnets in the non-secure network. If the non-secure network is the Internet, the NAT addresses need to come from a public network or subnet, in other words, the NAT addresses need to be assigned by IANA.
        The assigned addresses should be reversed in a pool, in order to use them when needed. If connections are established from the secure network, NAT can just pick the next free public address in the NAT pool and assign that to the requesting secure host. NAT keeps track of which internal IP addresses are mapped to which external IP addresses at any give point in time, so it will be able to map a response it receives from the external network into the corresponding secure IP address.
          When NAT assigns IP addresses on a demand basis, it needs to know when to return the external IP address to the pool of available IP addresses. There is no connection setup or tear-down at the IP level, so there is nothing in the IP protocol itself that NAT can use to determine when an association between a secure IP address and a NAT non-secure IP address is no longed needed. Since TCP is a connection-oriented protocol, it is possible to obtain the connection status information from TCP (whether connection is ended or not), whereas UDP does no include such information. Therefore, a timeout value should be configured that instructs NAT how long to keep an association in an indle state before returning the external IP address to the free NAT pool. Generally, the default value for this parameter is 15 minutes.
Network administrators also need to instruct NAT whether all the secure hosts are allowed to use NAT or not. This can be done by using corresponding configuration commands. If hosts in the non-secure network need to initiate connections to hosts in the secure network, NAT should be configured in advance as to which non-secure NAT address matches which secure IP address. Thus, a static mapping should be defined to allow connections from non-secure networks to a specific host in the internal network. The external name server may, for example, have an entry for a mail gateway that runs on a computer in the secure network. The external name server resolves the public host name of the internal mail gateway to the statically mapped IP address (the external address), and the remote mail server sends a connection request to the IP address. When that request comes to NAT on the non-secure interface, NAT looks into its mapping rules to see if it has a static mapping between the specified non-secure public IP address and a secure IP address. If so, it translates the IP address and forwards the IP packet into the secure network to the internal mail gateway.
         Please note that the non-secure NAT addresses as statically mapped to secure IP addresses should not overlap with the addresses specified as belonging to the pool of non-secure addresses NAT can use on a demand basis.

         NAT works fine for IP addresses in the IP header. Some application protocols exchange IP address information in the application data part of an IP packet, and NAT will generally not be able to handle translation of IP addresses in the protocol. It should be noted that implementation of NAT for specific applications that have IP information in the application data is more sophisticated than the standard NAT implementations.

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Dynamic Host Configuration Protocol (DHCP)

          Every computer or device that connects to the Internet or to an IP network needs an IP address. Most users do not have the expertise to configure an IP address, subnet mask, and gateway. In addition, whenever a computer changes its location in the network, it must receive a new address. Somehow, the address assigned to each device and the addresses that are still available must both be tracked. Most companies do no have the time, resources, or staff to devote to managing such configurations. In addition, networks operate with a finite number of IP addresses. It is most efficient for a host to reserve an address only when it is using it.
          Dynamic Host Configuration Protocol (DHCP) enables hosts on an IP network, called DHCP clients, to lease a temporary IP address from a DHCP server. The server can also issue other configurations to the client that help it function on the network (such as the addresses of Domain Name System (DNS) and Windows Internet Naming Service (WINS) servers). This protocol helps reduce administrative overhead on an IP-based network.
         The ProCurve Secure Router can act as a DHCP server for hosts on directly connected subnets. Router interfaces can also act as DHCP clients and receive a dynamic address from a directly connected DHCP server.

          Understanding the basics of DHCP will help you understand and remember how to configure a DHCP pool. If you can track the DHCP process, you will also find it much easier to troubleshoot the router's DHCP activity.
The DHCP request process breaks down into four steps:
1. The client broadcasts a DHCPDISCOVER packet, requesting an IP address and other configurations.
2. The server responds with a DHCPOFFER, which includes an available network address.
3. The client sends a DHCPREQUEST, accepting the offer and requesting the complete configuration from the server.
4. The server responds with a DHCPACK, which includes:
- the agreed-upon network address
- a default gateway
- a lease time
- the address of one or more DNS servers (optional)
- the address of one or more WINS servers (optional)

         Depending on how you configure the ProCurve Secure Router, the router can act as the DHCP server and/or one of its interfaces can act as a DHCP client (however, an interface that acts as a DHCP client cannot also act as a server).

The ProCurve Secure Router as a DHCP Server
          A router that also functions as a DHCP server is particularly useful for a small-to-medium site at which all subnets connect to the WAN router. The ProCurve Secure Router can connect to up to two switches on its Ethernet ports.

          You should configure one DHCP pool for each subnet. For the default gateway, you would specify the IP address of the Ethernet interface through which the router connects to the subnet.
The switches may also connect to several VLANs. In this case, you would configure VLAN support on the Ethernet interfaces. You would then create a DHCP pool for each VLAN.
           A WAN interface can also act as a server for DHCP clients. However, usually the router at the remote site or a DHCP server would act as the remote network's server. On the other hand, when you bridge two remote sites, one router should act as a DHCP server for all clients in the network.

The ProCurve Secure Router as a DHCP Client
          Some service providers require their subscribers to lease a dynamic address from them. In particular, Frame Relay service providers often require their costumers to use DHCP when connecting to their network. Each permanent virtual circuit (PVC) endpoint receives an IP address only when it needs it. This allows the service provider to conserve the limited number of IP addresses it owns. Internet service providers (ISPs) also often require subscribers to receive an IP address and other configurations from them.
         You must configure the interface that connects to such a provider to act as a DHCP client.
          Ethernet interfaces can also be DHCP clients on the connected subnet. Usually, it is a good idea to assign network nodes a static address.
Interfaces on the ProCurve Secure Router that can take a dynamic address are:
- Ethernet interfaces
- Frame Relay subinterfaces
- Asynchronous Transfer Mode (ATM) subinterfaces
- Point-to-Point Protocol(PPP) interfaces (only when brdging traffic)

            Rather than acting as the server for connected DHCP clients, the router can run DHCP relay, which allows hosts on one subnet to receive configurations from a server on a different subnet. The router receives DHCP packets from clients and forwards them to a remote server on behalf of the clients. Similarly, it receives the committed IP addresses from the server and forwards them to the clients.

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Sockets

Maybe you heard before or not about sockets. Today I am gonna talk a little about this subject

What is a socket?
You may have heard some UNIX hacker state, "Jeez, everything in UNIX is a file!". What that person may have been talking about is the fact that when UNIX programs do any sort of I/O (input/output), they do it by reading or writing to a file descriptor. A file descriptor is simply an integer associated with an open file. But, that file can be a network connection, a FIFO, a pipe, a terminal, a real on-the-disk file, or just about anything else. Everything in UNIX is a file! So when you want to communicate with another program over the Internet you're gonna do it through a file descriptor.
You make a call to the socket() system routine. It returns the socket descriptor, and you communicate through it using the specialized send() and recv() socket calls.

Question: "If it's a file descriptor why can't I just use the normal read() and write() calls to communicate through the socket?"
Answer: You ca, but send() and recv() offer much greater control over your data transmission.

There are all kinds of sockets:
- Internet Sockets
- UNIX Sockets
- X.25 Sockets
- etc.

There are a lot of Internet sockets, but I am gonna talk about only two in this post:
- Stream Sockets (SOCK_STREAM)
- Datagram Sockets (SOCK_DGRAM) or Connectionless Sockets

Stream sockets are reliable two-way connected communication streams. If you output two items into the socket in the order "1, 2", they will arrive in the order "1, 2" at the opposite end. They will also be error-free.

Question: "What uses stream sockets?"
Answer: Well, you may have heard of the telnet application; it uses stream sockets. All the characters you type need to arrive in the same order you type them. Also, web browsers use the HTTP protocol which uses stream sockets to get pages.

Question: "How do stream sockets achieve this high level of data transmission quality?"
Answer: They use a protocol called "The Transmission Control Protocol" otherwise knows as TCP. TCP makes sure your data arrives sequentially and error-free. You may have heard "TCP" before as the better half of "TCP/IP" where IP (Internet Protocol) deals primarily with Internet routing and is not generally responsible for data integrity.

Datagram sockets: if you send a datagram, it may arrive. It may arrive out of order. If it arrives, the data whithin the packet will be error-free.
Datagram sockets also use IP for routing, but they don't use TCP; they use the "User Datagram Protocol" (UDP).

Question: Why are Datagram sockets connectionless?
Answer: Well, basically, it's because you don't have to maintain an open connection as you do with stream sockets. You just build a packet, slap an IP header on it with destination information, and send it out. No connection needed. They are generally used either when a TCP stack is unavailable or when a few dropped packets here and there don't mean the end of the Universe.
Sample applications: tftp(trivial file transfer protocol), dhcpcd(a DHCP client), multiplayer games, streaming audio, video conferencing, etc.
The TFTP and similar programs have their own protocol on top of UDP. For example, the TFTP protocol says that for each packet that gets sent, the recipient has to send back a packet that says, "I got it!"(an ACK packet). If the sender of the original packet gets no reply in a limited time, he'll re-transmit the packet until he finally gets an ACK. The acknowledgment procedure is very important when implementing reliable SOCK_DGRAM applications.
For unreliable applications like games, audio or video, you just ignore the dropped packets, or perhaps try to cleverly compensate for them.

Question: Why would you use an ureliable underlying protocol?
It's way faster to fire-and-forget than it is to keep track of what has arrived safely and make sure it's in order and all that. If you're sending chat messages, TCP is great; if you're sending 40 positional updates per second of the players in the world, maybe it doesn't matter so much if one or two get dropped, and UDP is a good choice.

References:
1. Beej's Guide to Network Programming - Copyright © 2015 Brian “Beej Jorgensen” Hall

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