Module 5: Number Systems

Binary Number System

Calculate numbers between decimal and binary systems

Hexadecimal Number System

Calculate numbers between decimal and hexadecimal systems

bits

Binary numbering system consists of 1s and 0s, called ?

0-9

Decimal numbering system consists of digits __ through __

• Hosts

• servers

• network equipment

what uses binary addressing to identify each other?

octets

Each address is made up of a string of 32 bits, divided into four sections called

32 bits

Each address is made up of a string of __ bits

dot

Each octet contains 8 bits (or 1 byte) separated by a ?

8 bits (or 1 byte)

Each octet contains _________ separated by a dot

dotted decimal

For ease of use by people, this dotted notation is converted to ?

Binary Positional Notation

means that a digit represents different values depending on the “position” the digit occupies in the sequence of numbers.

binary positional value table

is useful in converting a dotted decimal IPv4 address to binary.

128

Start in the ___ position (the most significant bit).

0, 64

If the position doesn’t starts in 128, record a binary __ in the 128 positional value and move to the __ positional value

1

If the position starts in 128, record a binary __ in the 128 positional value, subtract 128 from the decimal number, and move to the 64 positional value

1 0 1 0 1 0 0 0

what is the output?

Convert decimal 168 to binary

sabotable

Convert decimal 168 to binary (ANALYZE FLS)

• 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

binary

Routers and computers only understand ?

decimal

humans work in ?

128, 64, 32, 16, 8, 4, 2, 1

what are the positional value?

Binary to Decimal

steps (to convert ____ to ______):

1. multiply the binary and the positional value

2. add the result

Decimal to Binary

steps (to convert ____ to ______):

1. compare the decimal to the positional value

2. if greater than, enter 1 and subtract from the positional value

3. if less than, enter 0 and move on to the next positional value

4. repeat until no values left

Hexadecimal

is a base sixteen numbering system, using the digits 0 through 9 and letters A to F.

Hexadecimal

is used to represent IPv6 addresses and MAC addresses.

32 hexadecimal values

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 ?

Decimal to Hexadecimal

steps (to convert ____ to ______):

1. Convert the decimal number to 8-bit binary strings.

2. Divide the binary strings in groups of four starting from the rightmost position.

3. Convert each four binary numbers into their equivalent hexadecimal digit. (to convert multiply each binary to 2 ex.(1×2^3)+(1×2^2)+(0×2^1)+(0×2^0))

Hexadecimal to Decimal

steps (to convert ____ to ______):

1. Convert the hexadecimal number to 4-bit binary strings.

2. Create 8-bit binary grouping starting from the rightmost position.

3. Convert each 8-bit binary grouping into their equivalent decimal digit.