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 :352 just a look.Do you know any tricks or easy way?

Answer 1

352 = 11 times 32.

11 is 1011 in binary (8+2+1).

32 is 2^5, so I add 5 zeros. 352 is 101100000.

Answer 2

convert 352 to binary.

I find it easiest to convert first to octal.

It can be seen that 5*8^2 +4*8^1 + 0 *8^0 =352
Thus 352 decimal is 540 octal

Now knowing that 0=000
1=001
2=010
3=011
4=100
5=101
6=110
7=111

Just substitute the binary value above for each octal digit of 540 to get:

101100000 binary = 352

To check your conversion fro decimal to octal, simply multiply 8 times the first digit and get 8*5=40. Then add the second digit and get 40+4=44. Then multiply that by 8 and get 8*44=352, then add last digit and get 352+0=352.

Answer 3

you need to remember these and generate such:

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32 and so on

N=352
step 1:
what is the nearest power of 2 below N?
step 2:
subtract it from N. Let it be new N. Goto step 1 till N become 1

here
N=352
nearest power of 2 = 256 = 2^8 (so the binary must have 9 digits)
N=352-256 = 96
nearest power of 2 = 64 = 2^6
N=96-64=32
nearest power of 2 = 32 = 2^5
so the 9th, 7th and 6th positions (from right) will have value of 1 and the rest 0
so 352 = 101100000

alternate method:
step 1: if N is even, put 0; else 1
step 2: divide N by 2; discard remainder if any; repeat step 1 till N=1

N=352
even - so, 0
divide by 2 -> 176 -> even so, 0
divide by 2 -> 88 -> even so, 0
divide by 2 -> 44 -> even so, 0
divide by 2 -> 22 -> even so, 0
divide by 2 -> 11 -> odd so, 1
divide by 2 -> 5 -> odd so, 1
divide by 2 -> 2 -> even so, 0
divide by 2 -> 1 -> odd so, 1

write down the results (reverse order) to get 101100000