Lec07_Number Systems.pptx

LEC07: NUMBER 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...

LEC07: NUMBER 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: 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 10 10 10 10 Position in Number 3 2 1 0 Calculate (103 ) (102) (101 ) (100) Position Value 100 0 100 10 1 Thousands Hundred s Tens Ones Positional Value 1000 100 10 1 Decimal Number (1234) 1 2 3 4 Calculate 1 x 1000 2 x 100 3 x 10 4x1 Add them up… 1000 + 200 + 30 +4 Result Radix: the base of a system of numeration. 1,234 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 (27) (26) (25) (24) (23) (22) (21) (20) 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 1x6 4 0x3 2 0x1 6 0x8 0x4 0x2 0x1 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 1x12 8 1x6 4 0x3 2 0x1 6 0x8 0x4 0x2 0x1 Add Them Up… 128 + 64 +0 +0 +0 +0 +0 +0 Binary Number (10101000) 1 0 1 0 1 0 0 0 Calculate 1x12 8 0x6 4 1x3 2 0x1 6 1x8 0x4 0x2 0x1 Add Them Up… 128 +0 + 32 +0 +8 +0 +0 +0 Binary Number (00001011) 0 0 0 0 1 0 1 1 Calculate 0x12 8 0x6 4 0x3 2 0x1 6 1x8 0x4 1x2 1x1 Add Them Up… 0 +0 +0 +0 +8 +0 +2 +1 Binary Number (00001010) 0 0 0 0 1 0 1 0 Calculate 0x12 8 0x6 4 0x3 2 0x1 6 1x8 0x4 1x2 0x1 Add Them Up… 0 +0 +0 +0 +8 +0 +2 +0 192 168 192.168.11. 10 11 10 Binary Number System : Decimal to Binary Conversion The binary positional value table is useful in converting a dotted decimal IPv4 address to binary. Start in the 128 position (the most significant bit). Is the decimal number of the octet (n) equal to or greater than 128? If no, record a binary 0 in the 128 positional value and move to the 64 positional value. If yes, record a binary 1 in the 128 positional value, subtract 128 from the decimal number, and move to the 64 positional value. Repeat these steps through the 1 positional value. 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 IPv6 address, with each X representing four hexadecimal values. Each four hexadecimal character group is referred to as a hextet. Hexadecimal Number System: Hexadecimal Conversions Decimal 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. to 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 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 is decimal THANKS! Best Regards!