Humans are most comfortable working in base ten $($decimal$),$ but it$$s important to remember that base two $($binary$)$ is the language of computers. In this lab, we$$ll perform some simple conversions between decimal and binary. We$$ll use examples seen when dealing with IPv$4$ addressing, in which the conversion is critical to understanding the organization of a network. To complete the assignment, upload a Word $(.$docx$)$ or Adobe $(.$pdf$)$ file with answers to the numbered problems below as your submission to this assignment in Blackboard. To get the most out of this lab, you should attempt to complete each conversion by hand, but it is acceptable and recommended to check your work using a calculator app as described in the presentation.

Binary digits, which can be only $0$ or $1,$ are referred to as bits. In computer networking, binary numbers are often expressed as groups of $8$ bits, referred to as a byte or$,$ in the context of an IPv$4$ address, as an octet. It is convenient to remind ourselves of the digital values of each of the $8$ bit positions in an octet:

Binary position $2726252423222120$

Decimal value $1286432168421$

Let$$s start with some practice problems we$$ll work together:

Practice #$1.$ Convert the binary number $10101010$ to decimal

$10101010=(1*128)+(0*64)+(1*32)+(0*16)+(1*8)+(0*4)+(1*2)+(0*1)$

$=128+32+8+2=170$

Practice #$2.$ Convert the binary number $01110111$ to decimal

$01110111=(0*128)+(1*64)+(1*32)+(1*16)+(0*8)+(1*4)+(1*2)+(1*1)$

$=64+32+16+4+2+1=119$

Note that the lowest $8-$bit value of $00000000=0$ decimal, while the highest value of $11111111=255$ decimal. This is why the individual octets of IPv$4$ addresses are between $0$ and $255.$

Calculate the decimal equivalents of the following binary numbers:

$1.11011011$

$2.01111111$

$3.10000000$

$4.11000000$

$5.11001101$

Now let$$s practice converting decimal values to binary. Refer to the M$00$ presentation, Binary Review for a walk through of the following methodology.

Practice #$3.$ Convert the decimal number $60$ to binary

$60/2=30$ R $0$

$30/2=15$ R $0$ Reading from the bottom, we get $111100$

$15/2=7$ R $1$

$7/2=3$ R $1$ We front load this with zeroes to write the answer in the traditional

$3/2=1$ R $18-$bit format of $00111100$

$1/2=0$ R $1$

Practice #$4.$ Convert the decimal number $182$ to binary

$182/2=91$ R $0$

$91/2=45$ R $1$ Reading from the bottom, we get $10110110,$ which is in $8-$bit format

$45/2=22$ R $1$

$22/2=11$ R $0$

$11/2=5$ R $1$

$5/2=2$ R $1$

$2/2=1$ R $0$

$1/2=0$ R $1$

Calculate the binary equivalents of the following decimal numbers:

$6.126$

$7.128$

$8.191$

$9.192$

$10.223$