6.2 Hexadecimal Numbers 6.2.1 Hexadecimal numbers as MAC addresses Instructor Note The purpose of this target indicator is to justify for the students the learning of a third number system. While it may seem abstract and of questionable use, the students will need to read hexadecimal numbers when troubleshooting LANs and when configuring routers. Also, hexadecimal is used extensively in other computer fields so it cannot hurt the student to have this extra knowledge. You have already studied the decimal and binary numbering systems. Decimal numbers express a Base 10 system, and binary numbers express a Base 2 system. Another numbering system you need to learn is the hexadecimal (hex) or base 16 system. You will learn about the hex numbering system on the following pages. Hex is a shorthand method for representing the 8-bit bytes that are stored in the computer system. It was chosen to represent identifiers because it can easily represent the 8-bit byte by using only two hexadecimal symbols. MAC addresses are 48 bits in length and are expressed as twelve hexadecimal digits. The first six hexadecimal digits, which are administered by the IEEE, identify the manufacturer or vendor and thus comprise the Organizational Unique Identifier (OUI). The remaining six hexadecimal digits comprise the interface serial number, or another value administered by the specific vendor. MAC addresses are sometimes referred to as burned-in addresses (BIAs) because they are burned into read-only memory (ROM) and are copied into random-access memory (RAM) when the NIC initializes.To learn more about how these OUIs are assigned, and to search for current address assignments, go to: Web Links OUIs Frequently Asked Questions Hex (hexadecimal) Explained 6.2 Hexadecimal Numbers 6.2.2 Basic hexadecimal (hex) numbering Instructor Note This target indicator builds upon the student's knowledge of decimal and binary. Indeed, the presentation is in the same format. Remind the students that decimal is base 10 and has certain rules revolving around the powers of ten; binary is base 2 and has certain rules revolving around the powers of 2; and hopefully hexadecimal, which is base 16 and has certain rules revolving around powers of 16 will seem less strange. Two-digit hex numbers are all that are needed for MAC address so there is no need to complicate matters with larger hexadecimal numbers. Hexadecimal is a Base 16 numbering system that is used to represent MAC addresses. It is referred to as Base 16 because it uses sixteen symbols; combinations of these symbols can then represent all possible numbers. Since there are only ten symbols that represent digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the Base 16 requires six more symbols, the extra symbols are the letters A, B, C, D, E, and F. The position of each symbol, or digit, in a hex number represents the base number 16 raised to a power, or exponent, based on its position. Moving from right to left, the first position represents 160, or 1; the second position represents 161, or 16; the third position, 162, or 256; and so on.Example: 4F6A = (4 x 163)+ (F[15] x 162)+ (6 x 161)+ (A[10] x 160) = 20330 (decimal) 6.2 Hexadecimal Numbers 6.2.3 Converting decimal numbers to hexadecimal numbers Instructor Note The purpose of this target indicator is for the student to demonstrate the ability to convert decimal numbers from 0 to 255 into two-digit hexadecimal numbers. An algorithm is given in flowchart form; but whichever way the student learns the conversion (except a calculator) is acceptable. The only known way to really learn this is practice! As with binary numbers, converting from decimal to hex is done with a system called the remainder method. In this method we repeatedly divide the decimal number by the base number (in this case 16). We then convert the remainder each time into a hex number. Example:Convert the decimal number 24032 to hex. 24032/16 = 1502, with a remainder of 0 1502/16 = 93, with a remainder of 14 or E 93/16 = 5, with a remainder of 13 or D 5/16 = 0, with a remainder of 5 By collecting all the remainders backward, you have the hex number 5DE0. 6.2 Hexadecimal Numbers 6.2.4 Converting hexadecimal numbers to decimal numbers Instructor Note The purpose of this target indicator is for the student to demonstrate the ability to convert hexadecimal numbers from 00 to FF into their decimal equivalents. An algorithm is given in flowchart form; but whichever way the student learns the conversion (except a calculator) is acceptable The only known way to really learn this is practice! Convert hexadecimal numbers to decimal numbers by multiplying the hex digits by the base number of the system (Base 16) raised to the exponent of the position. Example: Convert the hex number 3F4B to a decimal number. (Work from right to left.)3 x 16 x 16 x 16 = 12288 F(15) x 16 x 16 = 3840 4 x 16 = 64 B(11) x 16 = 11 _________________ 16203 = decimal equivalent 6.2 Hexadecimal Numbers 6.2.5 Methods for working with hexadecimal and binary numbers Instructor Note The purpose of this target indicator is to summarize the knowledge just acquired. There are two methods of converting binary numbers to hex numbers. The first is to convert binary to decimal, and then convert decimal to hex, using the methods you have already learned. The second method is to use a scientific calculator. It is important that you know how to do decimal, binary, and hexadecimal conversions without a calculator. In this course, the largest decimal number you have to deal with is 255; the longest binary number you have to deal with is 8 bits (11111111); and the largest hexadecimal number is 2 hex digits (FF). You must be able to do these calculations quickly, and do them in your head, both for practical purposes and for your exams.
