11base x +10base y=10001base 2

Question

10base x + y=10base 2
Plz solve and leave your ans in base 2

Answer 1

To solve the given system of equations, we can first rewrite the equations in base 10 form:

11x + 10y = 10001.
10x + y = 10.

Next, let's solve the system using the elimination method:

Multiply the second equation by 10: 10(10x + y) = 10(10).
This simplifies to: 100x + 10y = 100.

Subtract the second equation (100x + 10y = 100) from the first equation (11x + 10y = 10001):
(11x + 10y) - (100x + 10y) = 10001 - 100.
This simplifies to: -89x = 9901.

Divide both sides by -89:
x = 9901 / -89.

Converting 9901 to base 2:
9901 = 1 * 2^13 + 1 * 2^10 + 1 * 2^9 + 1 * 2^7 + 1 * 2^6 + 1 * 2^4 + 1 * 2^0.
9901 in base 2 is 10011010110101.

Converting -89 to base 2:
Since -89 is negative, we can find its base 2 representation using two's complement.
First, convert 89 to base 2:
89 = 1 * 2^6 + 0 * 2^5 + 1 * 2^4 + 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0.
89 in base 2 is 1011001.

Next, invert the digits (change 0 to 1 and 1 to 0) to get: 0100110.

Finally, add 1 to the inverted number: 0100110 + 1 = 0100111.

Therefore, -89 in base 2 is 0100111.

So, x = 10011010110101base 2 and y = 0100111base 2.