23basen= 1111base2 , find n
To find n, we can start by converting both numbers to their decimal forms.
1111 base 2 = 1*(2^3) + 1*(2^2) + 1*(2^1) + 1*(2^0) = 8 + 4 + 2 + 1 = 15
Now, we know that 23 base n = 15.
To convert 23 base n to decimal, we use the formula:
23 = 2*(n^1) + 3*(n^0)
Simplifying the equation, we get:
23 = 2n + 3
Subtracting 3 from both sides:
20 = 2n
Dividing both sides by 2:
10 = n
Therefore, n = 10.
2n +3=15 collecting like terms
2n=15-3
=12
Divide both sides by 2
2n÷2=12÷2
=6
Therefore, n=6
Apologies for the error in my previous response. You are correct, after collecting like terms and solving the equation, we find that n = 6. Thank you for pointing out the mistake.
Its my pleasure
Thank you for understanding. If you have any more questions, feel free to ask!
To find the value of n in the equation 23base n = 1111base 2, we need to convert both numbers to base 10 and solve for n.
First, let's convert 23base n to base 10:
23base n = 2*n^1 + 3*n^0
Next, we convert 1111base 2 to base 10:
1111base 2 = 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0 = 8 + 4 + 2 + 1 = 15
Now, we can set up the equation:
2*n^1 + 3*n^0 = 15
Simplifying the equation:
2n + 3 = 15
2n = 15 - 3
2n = 12
n = 12/2
n = 6
Therefore, the value of n is 6.
To convert the number 23 from base-n to base-2, we need to find the value of n.
First, let's break down the given equation:
23 (base-n) = 1111 (base-2)
To convert 1111 from base-2 to decimal, we can use the positions of the digits. In base-2, each digit represents a power of 2, starting from the rightmost digit:
(1 * 2^3) + (1 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 4 + 2 + 1 = 15
So, 1111 (base-2) = 15 (decimal).
Now let's convert 23 (base-n) to decimal. We cannot directly convert it unless we know the value of n. However, we can establish an equation using the positional representation of the digits:
(2 * n^1) + (3 * n^0) = 15
Simplifying this equation:
2n + 3 = 15
Now, isolate the variable n:
2n = 15 - 3
2n = 12
n = 12 / 2
n = 6
Therefore, n is 6.