i know this seems selfish but anyone know the answer to this math problem?

Question

my math teacher is useless. he doesnt teach us how to solve things and like he would give us a problem, and we have no idea whats hes talking about helppp mEE.

the problem is

N is the greatest 6-digit base 2 number
P is the least 6 digit base 2 number
whats N-P?

sorry i know this seems wrong but i really need help.

Answer 1

N = 111111 in binary (base 2)
N = 63 (base 10)
P = 100000 (base 2)
any smaller number will make it 5 or less digits
P = 32 (base 10)
N-P = 31 (base 10)
N-P = 011111 (base 2)

Answer 2

N is 111111; P is - 111111 so N - P is (adding the opposite of the subtrahend):
0 1 1 1 1 1 1
0 1 1 1 1 1 1
-----------------
1 1 1 1 1 1 0 base 2

(I had to use leading zeros in order to keep columns straight.)

Though it's not necessary, that base 2 difference is equal to base 10, 126. I am guessing that the teacher might be pushing to "untie" you from base 10. After all, the addition tables/ flash cards for base 2 are pretty simple:
0+0 = 0; 0 + 1 = 1; 1 + 1 = 10; just give your answer in base 2.

Answer 3

N = 111111(base 2) = 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 1
P = 100000(base 2) = 2^5

N - P = 31

You can also do it by combination:
(2^6 -1) - 2^5 = 31

The second way can be extended to n digit base 2 number:
(2^n - 1) - 2^(n - 1)

Answer 4

Base 2 just uses 1s and 0s. Just write the largest and smallest six digit numbers and subtract.

N = 111111
P = 100000

N - P = 11111

If this still seems unclear let me give you a similar problem using base 10. Write the largest and smallest six digit numbers and subtract.

x = 999999
y = 100000

x - y = 899999

x is the largest because we used the largest digit, 9 in all the places.

y is the smallest because we used the smallest non zero digit, 1 in the first place (if we had used 0 it wouldn't be a six digit number) and the smallest digit, 0 everywhere else.

Do the same in base 2, but all you have to work with is 1s and 0s.

Answer 5

N = 111111
P = 100000
N - P = 011111 or '31' in base 10 (1+2+4+8+16 = 31)



;-)

Answer 6

Base 2 uses 0's and 1's. So, the greatest 6 digit number would be 00111111, which is 63. The least would probably be 0.
So 63-0=63

I'm guessing the answer is 63.

Answer 7

N = 111111
P =100000

N-P = 11111 ..... I guess this it what you're looking for ;)

P.S.: Base 2 means you can only use 0 and 1 ....