05_Number Systems Flashcards
Binary Number System
Calculate numbers between decimal and binary systems.
- Binary is a numbering system that consists of the digits 0 and 1 called bits.
- Binary is important for us to understand because hosts, servers, and network devices use binary addressing. Specifically, they use binary IPv4 addresses, as shown in the figure, to identify each other.
Each address consists of a string of 32 bits, divided into four sections called octets. Each octet contains 8 bits (or 1 byte) separated with a dot. For example, PC1 in the figure is assigned IPv4 address 11000000.10101000.00001010.00001010. Its default gateway address would be that of R1 Gigabit Ethernet interface 11000000.10101000.00001010.00000001.
Binary works well with hosts and network devices. However, it is very challenging for humans to work with.
For ease of use by people, IPv4 addresses are commonly expressed in dotted decimal notation. PC1 is assigned the IPv4 address 192.168.10.10, and its default gateway address is 192.168.10.1
Binary is a numbering system that consists of the numbers 0 and 1 called bits. In contrast, the decimal numbering system consists of 10 digits consisting of the numbers 0 – 9. Binary is important for us to understand because hosts, servers, and network devices use binary addressing, specifically, binary IPv4 addresses, to identify each other. You must know binary addressing and how to convert between binary and dotted decimal IPv4 addresses. This topic presented a few ways to convert decimal to binary and binary to decimal.
Hexadecimal Number System
Calculate numbers between decimal and hexadecimal systems.
To understand IPv6 addresses, you must be able to convert hexadecimal to decimal and vice versa.
Just as decimal is a base ten number system, hexadecimal is a base sixteen system. The base sixteen number system uses the numbers 0 to 9 and the letters A to F. The hexadecimal numbering system is used in networking to represent IPv6 addresses and Ethernet MAC addresses. IPv6 addresses are 128 bits in length and every 4 bits is represented by a single hexadecimal digit; for a total of 32 hexadecimal values. 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 also first convert the decimal to binary.
Positional notation
Learning to convert binary to decimal requires an understanding of positional notation. Positional notation means that a digit represents different values depending on the “position” the digit occupies in the sequence of numbers.
Which is the binary equivalent to the 192.168.11.10 IP address?
11000000.10101000.00001011.00001010
Which of the following is the binary equivalent to the 172.16.31.30 IP address?
10101100.00010000.00011111.00011110
Convert Binary to Decimal
To convert a binary IPv4 address to its dotted decimal equivalent, divide the IPv4 address into four 8-bit octets. Next apply the binary positional value to the first octet binary number and calculate accordingly.
binary positional value table
X = 128 - 64 - 32 - 16 - 8 - 4 - 2 - 1
Is the decimal number of the octet (n) equal to or greater than the most-significant bit (X)?
If no, then enter binary 0 in the X positional value.
If yes, then add a binary 1 in the X positional value and subtract X from the decimal number.
Decimal to Hexadecimal Conversions
Converting decimal numbers to hexadecimal values is straightforward. Follow the steps listed:
- 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.
The example provides the steps for converting 168 to hexadecimal.
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.
- 1010is hex A and 1000 is hex 8.
Answer: 168 is A8 in hexadecimal.
Hexadecimal to Decimal Conversion
Converting hexadecimal numbers to decimal values is also straightforward. Follow the steps listed:
- 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.
This example provides the steps for converting D2 to decimal.
- 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.
Answer: D2 in hexadecimal is 210 in decimal.
Which is the hexadecimal equivalent of 202?
CA
Which is the hexadecimal equivalent of 254?
FE
Which is the decimal equivalent of A9?
169
Which of the following is the decimal equivalent of 7D?
125
What is the binary representation for the decimal number 173?
10101101
Given the binary address of 11101100 00010001 00001100 00001010, which address does this represent in dotted decimal format?
236.17.12.10
