Sistemas de Numeración: Binario, Decimal y Hexadecimal, Resúmenes de Redes Inalámbricas

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Number Systems

Module Objectives

Module Title: Number Systems

Module Objective : Calculate numbers between decimal, binary, and hexadecimal systems.

Topic Title Topic Objective

Binary Number System Calculate numbers between decimal and binary

systems.

Hexadecimal Number System Calculate numbers between decimal and

hexadecimal systems.

Binary Number System

Binary and IPv4 Addresses

• (^) Binary numbering system consists of 1s and 0s, called bits
• (^) Decimal numbering system consists of digits 0 through 9
• (^) Hosts, servers, and network equipment using binary addressing to identify each other.
• (^) Each address is made up of a string of 32 bits, divided into four sections called octets.
• (^) Each octet contains 8 bits (or 1 byte) separated by a dot.
• (^) For ease of use by people, this dotted notation is converted to dotted decimal.

Binary Number System

Video – Convert Between Binary and Decimal Numbering

Systems

This video will cover the following:

• (^) Positional notation review
• Powers of 10 review
• (^) Decimal – base 10 numbering review
• (^) Binary – base 2 numbering review
• (^) Convert an P address in binary to decimal numbering

Binary Number System

Binary Positional Notation (Cont.)

The binary positional notation system operates as shown in the tables below.

Radix 2 2 2 2 2 2 2 2 Position in Number 7 6 5 4 3 2 1 0 Calculate (2^7 ) (2^6 ) (2^5 ) (2^4 ) (2^3 ) (2^2 ) (2^1 ) (2^0 ) Position Value 128 64 32 16 8 4 2 1 Positional Value 128 64 32 16 8 4 2 1 Binary Number (11000000) 1 1 0 0 0 0 0 0 Calculate 1x128 1x64 0x32 0x16 0x8 0x4 0x2 0x Add Them Up… 128 + 64 + 0 + 0 + 0 + 0 + 0 + 0 Result 192

Binary Number System

Convert Binary to Decimal

Convert 11000000.10101000.00001011.00001010 to decimal. Positional Value 128 64 32 16 8 4 2 1 Binary Number (11000000) 1 1 0 0 0 0 0 0 Calculate 1x128 1x64 0x32 0x16 0x8 0x4 0x2 0x Add Them Up… 128 + 64 + 0 + 0 + 0 + 0 + 0 + 0 Binary Number (10101000) 1 0 1 0 1 0 0 0 Calculate 1x128 0x64 1x32 0x16 1x8 0x4 0x2 0x Add Them Up… 128 + 0 + 32 + 0 + 8 + 0 + 0 + 0 Binary Number (00001011) 0 0 0 0 1 0 1 1 Calculate 0x128 0x64 0x32 0x16 1x8 0x4 1x2 1x Add Them Up… 0 + 0 + 0 + 0 + 8 + 0 + 2 + 1 Binary Number (00001010) 0 0 0 0 1 0 1 0 Calculate 0x128 0x64 0x32 0x16 1x8 0x4 1x2 0x Add Them Up… 0 + 0 + 0 + 0 + 8 + 0 + 2 + 0

Binary Number System

Decimal to Binary Conversion Example

• (^) Convert decimal 168 to binary Is 168 > 128?
  • (^) Yes, enter 1 in 128 position and subtract 128 (168-128=40) Is 40 > 64?
  • (^) No, enter 0 in 64 position and move on Is 40 > 32?
  • (^) Yes, enter 1 in 32 position and subtract 32 (40-32=8) Is 8 > 16?
  • (^) No, enter 0 in 16 position and move on Is 8 > 8?
  • (^) Equal. Enter 1 in 8 position and subtract 8 (8-8=0) No values left. Enter 0 in remaining binary positions 128 64 32 16 8 4 2 1 1 0 1 0 1 0 0 0 Decimal 168 is written as 10101000 in binary

Binary Number System

IPv4 Addresses

• (^) Routers and computers only understand binary, while humans work in decimal. It is important for you to gain a thorough understanding of these two numbering systems and how they are used in networking.

Hexadecimal Number System

Hexadecimal and IPv6 Addresses

• (^) To understand IPv6 addresses,

you must be able to convert

hexadecimal to decimal and

vice versa.

• (^) Hexadecimal is a base sixteen

numbering system, using the

digits 0 through 9 and letters A

to F.

• (^) It is easier to express a value

as a single hexadecimal digit

than as four binary bit.

• (^) Hexadecimal is used to

represent IPv6 addresses and

MAC addresses.

Hexadecimal Number System

Hexadecimal and IPv6 Addresses (Cont.)

• (^) IPv6 addresses are 128 bits in

length. Every 4 bits is

represented by a single

hexadecimal digit. That makes

the IPv6 address a total of 32

hexadecimal values.

• (^) The figure shows the preferred

method of writing out an IPv

address, with each X

representing four hexadecimal

values.

• (^) Each four hexadecimal

character group is referred to

as a hextet.

Hexadecimal Number System

Decimal to Hexadecimal Conversions

Follow the steps listed to convert decimal numbers to hexadecimal values:

• (^) Convert the decimal number to 8-bit binary strings.
• (^) Divide the binary strings in groups of four starting from the rightmost position.
• (^) Convert each four binary numbers into their equivalent hexadecimal digit.

For example, 168 converted into hex using the three-step process.

• (^) 168 in binary is 10101000.
• (^) 10101000 in two groups of four binary digits is 1010 and 1000.
• 1010 is hex A and 1000 is hex 8, so 168 is A8 in hexadecimal.

Hexadecimal Number System

Hexadecimal to Decimal Conversions

Follow the steps listed to convert hexadecimal numbers to decimal values:

• (^) Convert the hexadecimal number to 4-bit binary strings.
• (^) Create 8-bit binary grouping starting from the rightmost position.
• (^) Convert each 8-bit binary grouping into their equivalent decimal digit.

For example, D2 converted into decimal using the three-step process:

• (^) D2 in 4-bit binary strings is 1110 and 0010.
• (^) 1110 and 0010 is 11100010 in an 8-bit grouping.
• 11100010 in binary is equivalent to 210 in decimal, so D2 is 210 is decimal

Module Practice and Quiz

What did I learn in this module?

• (^) Binary is a base two numbering system that consists of the numbers 0 and 1, called bits.
• (^) Decimal is a base ten numbering system that consists of the numbers 0 through 9.
• (^) Binary is what hosts, servers, and networking equipment uses to identify each other.
• (^) Hexadecimal is a base sixteen numbering system that consists of the numbers 0 through 9 and the letters A to F.
• (^) Hexadecimal is used to represent IPv6 addresses and MAC addresses.
• (^) IPv6 addresses are 128 bits long, and every 4 bits is represented by a hexadecimal digit for a total of 32 hexadecimal digits.
• (^) 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 first convert the decimal to binary and then the binary to hexadecimal.