Binary Number System: Binary to Decimal Conversion
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Questions and Answers

What is the first step when converting a decimal number to binary?

  • Subtract 1 from the decimal number
  • Check if the decimal number is greater than 128 (correct)
  • Divide the decimal number by 2
  • Convert the decimal number to hexadecimal

    • What is the purpose of using hexadecimal in IPv6 addresses?

  • To make it easier to read and write (correct)
  • To increase the security of the address
  • To make it compatible with IPv4 addresses
  • To shorten the length of the address

    • How many bits are in an IPv6 address?

  • 256 bits
  • 512 bits
  • 64 bits
  • 128 bits (correct)

    • What is the advantage of using hexadecimal over binary?

    <p>It is easier to read and write</p> Signup and view all the answers

    What does a router understand?

    <p>Binary numbers</p> Signup and view all the answers

    What is the result of subtracting 128 from 168?

    <p>40</p> Signup and view all the answers

    What is the purpose of the binary number system?

    <p>To enable communication between routers and computers</p> Signup and view all the answers

    What is the decimal equivalent of the binary number 10101000?

    <p>168</p> Signup and view all the answers

    What is the radix of the Binary Number System?

    <p>2</p> Signup and view all the answers

    What is the position value of the 7th bit from the right in a binary number?

    <p>128</p> Signup and view all the answers

    What is the decimal equivalent of the binary number 11000000?

    <p>192</p> Signup and view all the answers

    How do you convert a binary number to decimal?

    <p>Multiply each bit by its positional value and add them up.</p> Signup and view all the answers

    What is the purpose of the binary positional value table?

    <p>To convert decimal to binary.</p> Signup and view all the answers

    What is the first step in converting a decimal number to binary using the binary positional value table?

    <p>Start in the 128 position.</p> Signup and view all the answers

    What do you record in the 128 positional value if the decimal number is less than 128?

    <p>A binary 0.</p> Signup and view all the answers

    What is the resulting IPv4 address after converting 192.168.11.10 to binary?

    <p>11000000.10101000.00001011.00001010</p> Signup and view all the answers

    What is the base of the decimal numbering system?

    <p>10</p> Signup and view all the answers

    What is the main purpose of using dotted notation in binary addresses?

    <p>To make it easier for people to understand</p> Signup and view all the answers

    What is the total number of bits in a binary address?

    <p>32</p> Signup and view all the answers

    What is the term for a digit representing different values depending on its position in a sequence of numbers?

    <p>Positional notation</p> Signup and view all the answers

    What is the total number of sections in a binary address?

    <p>4</p> Signup and view all the answers

    What is the value of the 'Thousands' position in the decimal positional notation system?

    <p>1000</p> Signup and view all the answers

    What is the term for a string of 8 bits in a binary address?

    <p>Octet</p> Signup and view all the answers

    What is the main advantage of using binary addressing in hosts, servers, and network equipment?

    <p>Used to identify each other</p> Signup and view all the answers

    How many bits are represented by a single hexadecimal digit?

    <p>4 bits</p> Signup and view all the answers

    How many hexadecimal values make up an IPv6 address?

    <p>32 hexadecimal values</p> Signup and view all the answers

    What is each four hexadecimal character group referred to as?

    <p>Hextet</p> Signup and view all the answers

    What is the first step in converting decimal numbers to hexadecimal values?

    <p>Convert the decimal number to 8-bit binary strings</p> Signup and view all the answers

    What is the result of converting 168 to hexadecimal using the three-step process?

    <p>A8</p> Signup and view all the answers

    What is the first step in converting hexadecimal numbers to decimal values?

    <p>Convert the hexadecimal number to 4-bit binary strings</p> Signup and view all the answers

    What is the result of converting D2 to decimal using the three-step process?

    <p>210</p> Signup and view all the answers

    How many bits are in each group when converting hexadecimal numbers to decimal values?

    <p>8-bit</p> Signup and view all the answers

    What is the purpose of the three-step process in hexadecimal conversions?

    <p>To convert decimal numbers to hexadecimal values</p> Signup and view all the answers

    What is the advantage of using the hexadecimal number system?

    <p>It is used for IPv6 addresses</p> Signup and view all the answers

    Study Notes

    Binary Number System

    • Binary numbering system consists of 1s and 0s, called bits
    • Decimal numbering system consists of digits 0 through 9
    • Hosts, servers, and network equipment use 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

    Decimal to Binary Conversion

    • To convert a decimal number to binary, start in the 128 position (the most significant bit)
    • If the decimal number is equal to or greater than 128, record a binary 1 in the 128 positional value and subtract 128 from the decimal number
    • Repeat these steps through the 1 positional value

    Binary Positional Notation

    • Positional notation means that a digit represents different values depending on the “position” the digit occupies in the sequence of numbers
    • The decimal positional notation system operates as shown in the tables below
    • Radix: the base of a system of numeration
    • In binary positional notation, every 4 bits is represented by a single hexadecimal digit

    IPv4 Addresses

    • Routers and computers only understand binary, while humans work in decimal
    • It is important to gain a thorough understanding of these two numbering systems and how they are used in networking
    • IPv4 addresses are 32 bits in length and divided into four sections called octets
    • Each octet contains 8 bits (or 1 byte) separated by a dot

    Hexadecimal Number System

    • 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 bits
    • Hexadecimal is used to represent IPv6 addresses and MAC addresses
    • IPv6 addresses are 128 bits in length

    Hexadecimal Conversions

    • 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
    • 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 to Decimal Conversions

    • 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
    • Example: D2 converted into decimal using the three-step process
      • D2 in 4-bit binary strings is 1101 and 0010
      • 1101 and 0010 is 11010010 in an 8-bit grouping
      • 11010010 in binary is equivalent to 210 in decimal, so D2 is 210 in decimal

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    Lec07_Number Systems.pptx

    Description

    Test your skills in converting binary numbers to decimal. Practice calculating positional values and converting binary numbers to decimal numbers.

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