Binary Number System: Binary to Decimal Conversion

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

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