Answer and prove you know many tricks?

Question

Suppose that i have no calculator and without any method or rule How can i understand whats the binary of this decimal :141 just a look.Do you know any tricks or easy way?

Answer 1

First try to figure out what is the largest power of two in the given number. in your example, it's 128 which is equal to 2^7.
The exponent of 2 signifies that we have a 7 bits or 7 combination of 1 and 0.
next, is subtract 128 from the given #.
that is,
141 - 128 = 13.
Now using the result, find the next largest power of 2. This is
8 which is equal to 2^3.
next, subtract again from the result
13-8=5.
then we have 4 which is 2^2.
subtract again.
5-4=1
thus the next power of 2 is 1 which is 2^0.

All the exponents signifies the the position of bit that is a high or equal to 1.

In your example 144 in binary is equal to

76543210>>>>pertains to the exponent of 2
10001101>>>>binary equivalent


Thus
144 (decimal) = 10001101 (decimal)

Isn't that simple.

You will figure it out from the start how large or how many bit will a given # of yours contain and you you will identify your MSB.

Instead of dividing by two which will give you the LSB.

Answer 2

You should have used a computer.


Anyway, if you have NO METHOD OR RULE, then definitely you cannot know the binary of that.
But, my quickest method is to find the highest power of 2 which is less than the number.
In this case 141, that is 128.
Then we subtract, we get 13.
The next power of 2 is 8.
We again subtract, we get 5.
The next power is 4.
We subtract, we get 1.
Then, the last is 1 (it is a power of 2).
Then, we write the number in the following order: 128, 64, 32, 16, 8, 4, 2, 1.
Then we put 1 for those numbers we have mentioned, otherwise we put 0. Therefore, the binary of the decimal 141 is:

1 0 0 0 1 1 0 1

^_^
^_^

Answer 3

Write down the powers of 2 until you are more than 1/2 way
to your target or exactly on it. In this case we have
1 2 4 8 16 32 64 128. Now starting from 128 and working backwards, subtract each number(if you can) from the previous result. Your first result is the target number itself - 141. If you
can subtract it, write down a 1 to the right of the previous digit.
If you can't(that's when your list number is greater than your
result) write down a zero. Let's go.
141-128=13
1
Can't subtract 64 or 32 or 16 from 13 so now it's
1000
Subtract 13-8=5 so now it's
10001
Subtract 5-4=1, now it's
100011
Can't subtract 2 from 1 so it's
1000110
Now subtract 1-1=0 and it's
10001101 and we're finished.
Pretty easy trick, huh?

Answer 4

May be this is the old style to solve, but it's not easy too.
Try to make sequence of binary:

2 x 2 x 2 x 2 x 2 x 2 x 2= 2^7......................... (keep)
4 x 4 x 4 x 2
16 x 8
128 ............................. 141-128 = 13

Since 13 = 8 + 3 = 2 x 2 x 2 + 2 + 1 = 2^3 + 2^1 + 1........... (keep)
Remember 1 = 2^0,
So if we combine becomes:

141 = (1 x 2^7) + (1 x 2^3) + ( 1 x 2^1) +(1 X 2^0) = 10001011
according to
^76543210
=10001011


I hope my answer is right.

Answer 5

well you could divide by 2 multiple times and get an answer but with a trick

you can think of hex numbers 16*8= 128 = 8 hex
141-128=13 dec

so 141 dec = 8d hex
Thus,

1000 1101 so were done

Answer 6

to convert any decimal no. to any other base just keep dividing by that no. and the remainder gives the converted no.

2 |_141
2 |_70-----1 ^
2 |_35----0 |
2 |_17---1 |
2 |_8----1 |
2 |_4---0 |
2 |_2--0 |
1----0 |
________|

hence the converted no is 1001101.

Answer 7

I think it is 47, but I may be off.