Number Systems

Numbers are symbols that we use to represent quantities.  Binary, octal, decimal and hexadecimal are four number systems used frequently in computing and networking.   This set of short tutorials on number systems will explore the binary, decimal and hexadecimal number systems. You will need to understand all of them for the CCNA exam, but most especially binary and hexadecimal.  Decimal is the human numbering system we display IPv4 addresses.  Binary is used for calculating network masks, hexadecimal is used to display Ethernet MAC addresses and IPv6 addresses.

 

Number Systems:  Decimal

We humans use the base-10 number system, also called ‘decimal’.   This is the number system we are all familiar with.  We use the the following symbols for this number system:   0, 1, 2, 3, 4, 5, 6, 7, 8, 9  We draw these ‘symbols’ when we want to represent quantities of things we can count, such as a dozen eggs (12 eggs).   When we have more than 10, we use two or more columns of numbers, such as 12, which is 10 of something plus 2 more.  All number systems use symbols and all of them use columns to represent larger and larger values.

To access this complete online tutorial, click here:  Decimal Number System tutorial

Number Systems: Binary

There are other ‘number systems’ and computers use a number system called ‘binary’.  There are just two number symbols in binary: 0 and 1.  Since there are only 2 symbols, it is also called base-2. Once you have learned binary, you will find it much easier to do things such as calculating subnet masks and network ranges.

There will be no questions on binary itself in the certification tests. However, you must understand binary,  be able to convert from binary to decimal to answer questions on networks, subnets and binary masks.

To access this entire online tutorial, click here:  Binary Tutorial series (8 tutorials)


Number Systems: Hexadecimal

Hexadecimal is the next most frequently used number system. “hex” means six, “decimal” is ten, and so hexadecimal is a base-16 number system. Computers use hexadecimal for bytecode, memory dumps, physical MAC addresses on network cards and logical Internet Protocol v6 (IPv6) addresses to name a few of the many ways hexadecimal is used. Hexadecimal uses the the same symbols as decimal (0-9), plus a few extras (A-F). For every column in this number system, you may see any of the following: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, A, B, C, D, E, F. Each hexadecimal digit is used to represent 4 bits, two hexadecimal digits represent one byte, so hexadecimal digits are often grouped in pairs or quads. Media Access Control addresses (MAC addresses) are frequently listed as six pairs of hexadecimal numbers separated by colons (BA:DB:EE:F0:12:A3).

To access this complete online tutorial, click here:  Hexadecimal Number System tutorial

Next week we will introduce you to basic networking concepts and the two reference models for networking, the OSI Reference Model and the TCP/IP Model.

 

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