Mastering Binary Math

Cisco certification candidates, from the CCNA to the CCIE, must master binary math. This includes basic conversions, such as binary-to-decimal and decimal-to-binary, as well as more advanced scenarios involving subnetting and VLSM. There’s another conversion that might rear its ugly head on your Cisco exam, though, and that involves hexadecimal numbering. Newcomers to hexadecimal numbering are often confused as to how a letter of the alphabet can possibly represent a number. Worse, they may be intimidated – after all, there must be some incredibly complicated formula involved with representing the decimal 11 with the letter “b”, right? Wrong. The numbering system we use every day, decimal, concerns itself with units of ten. Although we rarely stop to think of it this way, if you read a decimal number from right to left, the number indicates how many units of one, ten, and one hundred we have. That is, the number “15” is five units of one and one unit of ten. The number “289” is nine units of one, eight units of ten, and two units of one hundred. Simple enough! Units Of 100 0 2 Units Of 10 1 8 Units Of 1 5 9

The decimal “15” The decimal “289”

Hex numbers are read much the same way, except the units here are units of 16. The number “15” in hex is read as having five units of one and one unit of sixteen. The number “289” in hex is nine units of one, eight units of sixteen, and two units of 256 (16 x 16). Units Of 256 0 2 Units Of 16 1 8 Units Of 1 5 9

The hex numeral “15” The hex numeral “289”

Since hex uses units of sixteen, how can we possibly represent a value of 10, 11, 12, 13, 14, or 15? We do so with letters. The decimal “10” is represented in hex with the letter “a”; the decimal 11 with “b”; the decimal “12” with “c”, “13” with “d”, “14” with “e”, and finally, “15” with “f”. (Remember that a MAC address of “ffff.ffff.ffff” is a Layer 2 broadcast.) Practice Your Conversions for Exam Success Now that you know where the letters...