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Conversion from Binary to Decimal

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for the conversion conversion from

system is the internal language

of electronic computers

so these are the steps

how to use positional notation so we

have one zero zero one one

and i may be sign two so first write

down the binary number and list the power

power

of two from left to right

so let's say we we want to convert the

binary numbers

one zero zero one one zero one one base

of two to decimal

first write it down then write down the

powers of 2 from right to left

so i start at 2 raise to 0 degrees

no raise to 0 not zero degrees raised to zero

zero

i'm reading it as one so increment

the exponent by one from each

power so it stops

stop when the amount of elements in

list is equal to the amount of digits in the

the

binary numbers or number i mean

so the example number one zero zero one one

one

zero one one has eight digits so the list

list

with eight elements would like look like this

this

one twenty eight three sixty four thirty

two six one

sixteen eight four two one four

two one so panopoulo remember [Music]

to the 6 is 64 2 to the p 32 to the

fourth 16

to the three is eight to the square root is

four to the one is two and two three

zero is one so yeah okay next step

write the digits of the verani number

below the the corresponding

powers of two you can get another

argument so

now just write one zero zero one one

zero one one below the

numbers so 1 28 64 32 16

8 4 and 2 and 1 so that

each binary digit corresponds with each

power of two

so the one to the right of the binary

number should

correspond with the one on the right of

the listed

powers of two and so on so you can

also write the binary digits above the

powers of two

if you prefer it that way so what is

important is that

they match up you know important

okay so for example one

zero zero one one zero one one okay

so next connect the digits in the binary

number with their corresponding powers

of two

so draw a line starting from the right

connecting each consecutive digit

of the binary number to the power of

two that is next is the least above its

begin by drawing a line from the first

digit of the binary number

to the first power of two in the fourth list

list

above it then draw a line from the

second digit of the binary number

to the second power of two in the fleece

continue connecting each digit with each

corresponding power of two this will

help you

visually see the relationship between

the two sets of

step four write down the final value of each

each

power of two so move through each digit

of the binary number if the digit is

a one write its corresponding power of

two below the line

under the line of the digit if the digit

is a zero right zero below the line

under the digit

so since one corresponds with one it becomes

becomes

a one since two corresponds with one it

becomes two

since four corresponds with zero it

becomes zero shameful any number that

multiplies zero is zero

so since a is corresponds with one it

becomes eight

since 16 corresponds with one it becomes

16 so 32 corresponds to zero it becomes zero

zero

and 64 corresponds with zero and

therefore becomes zero

while 128 corresponds with one so n

becomes one weight one way i'm getting

so remember 128 times 1 is

128. 64 times 0 is

0 32 times 0 is 0. 16 times

1 is 16 8 times 1 is 8

four times zero is zero two times one is two

two

and then one times one is one so it

takes a good

next step five add the final value so

now the

add the like the number written below

the line so here was

it to do is 128 plus 0 plus 0 plus 16 plus

plus

8 plus 0 plus 2 plus 1 is equal to 155

so this is the decimal equivalent of the

little binary number is not it

so write the answer along with b

subscript so now all

you have to do is write 150 by 10

for the decimal procedure so show that

they are working with the decimal answer

so which must be operating in powers of

10. so the more you get

used to converting from binary to

decimal the more easy

it will be you for you to memorize the

power of two

so and you'll be able to complete the

tasks more quickly

anybody remember for here yeah i think

final answer nothing

so what are 55 bits of that in subscript yeah

for example use this method to convert a

binary number

with a decimal point to decimal form

so we have 1.1 base of two so you can

use this method

when you want to convert a binary number

such as 1.2

no what one point one base of two

decimals so all you have to do is

know the number on the left side of the decimal

decimal

is in in the units position like normal

while the number of the right side of

the decimal is in the

half's position for example one times

one half percent

diva so at the end so

the one to the left of the decimal point

is equal to 2

raised to 0 or 1 because

any number that 3 is 0 is 1. so the 1 to the

the

right of the decimal is equal to 2

raised to negative 1 which is 0.5

and add up one and five

and you'll get 1.5 which is equivalent

to 1.1

in decimal notation so i'm going to n

so 1.1 so

2 is zero and so this one

super canon attend one

zero is one plus

and 2 raised to negative 1 times 1 is 0.5

0.5

so we have again at that end we have 1.5

base of 10 because of the procedure nothing

nothing

so first write down the binary numbers

so this method does not use powers as such

such

it is simpler for converting a large

number in your

head because you only need to keep track

of a subtotal

so the first thing you need to do is to

write down the binary number

you'll be converting using a doubling method

method

let's say that the number you're working

is one zero one one

zero zero one we have base two

and subscript now write down okay so

second step starting from the left

double your previous total and at the

current digit so since you're working

with the binary number one zero one one zero

zero

zero one base of two your first digit

all the way on the left is one so your

previous total is zero

so since you haven't started yet you'll

have to double the previous total

zero and add one so the current digit is zero

zero

times two plus one is equal to one so your

your

so next step so double your current

total and at

the next leftmost digit so your current

total is one now

and the new current digit is zero so double

double

one and adds

zero so one times two plus zero is equal to

so repeat the previous steps just keep

going next double your current total and

add one

your next uh your next digit so two

times two plus one is equal to five your

current total

so we have 11 so your new total is 11

double your current 11 and then add zero

so equals

so we have equals to 22

and 22. so next step

repeat double your current total and add

zero so we have 44

plus or times two double dot attend plus

and zero another zero it's equal to 44.

next step so continue doubling your

current and

total and adding the next digit until

you run out of the

dates so now you're down to

your last number and are almost done so

all you have to do is take your current

total with 44 and double it

along adding one so the last digit which

is what

44 times 2 plus 1 is equal to 89 you're

all done so you

convert it 1 0 0 1 0 1 1 0 0 1

base of 2 to decimal notation to its

which is equal to 89

so okay so you're

write your final answer we have to show

that you are

working with a decimal so which has a base

base

of 10. so you finally answering more

okay next i'll use this method to convert

convert

it from any base to decimal so for example

example

doubling is used because the given

number is base of two

if the given number is it of different

base replace the two

indeed method with the base of the given

number for example we

if the given number is in the base of 37

so you you replace the the times 2

with times 37 so the final result will be

in decimal so we have the base of 10 for example

example

times 37 plus

1 which is equal to one because it

zero times thirty seven is zero so plus

one is equal to

so one times thirty seven plus

two so we have 39.

times 37 plus

39 37 plus 3 is 1 46

so this will be your final answer with

base of

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Conversion from Binary to Decimal