If (1P03)base 4=115 base 10, find p
To solve this problem, we need to convert the number (1P03) from base 4 to base 10 and then find the value of the digit "P".
To convert (1P03) from base 4 to base 10, we can use the position-value system.
The position-value system in base 4 is as follows:
(1P03)base 4 = 1 × 4^3 + P × 4^2 + 0 × 4^1 + 3 × 4^0
(1P03)base 4 = 64 + 4P + 0 + 3
We know that (1P03)base 4 = 115 base 10.
Therefore, we can write the equation:
64 + 4P + 0 + 3 = 115
Simplifying the equation:
67 + 4P = 115
Subtracting 67 from both sides:
4P = 115 - 67
= 48
Dividing both sides by 4:
P = 48 / 4
= 12
Therefore, the value of the digit "P" is 12.
To find the value of P, we need to convert the number (1P03)base 4 to base 10.
In base 4, each digit represents a power of 4. The powers start from right to left as 0, 1, 2, 3, and so on.
So, let's break down the number (1P03)base 4:
(1P03)base 4 = 1 * 4^3 + P * 4^2 + 0 * 4^1 + 3 * 4^0
Now, let's convert this to base 10:
(1P03)base 4 = 1 * 4^3 + P * 4^2 + 0 * 4^1 + 3 * 4^0
= 64 + 16P + 0 + 3
= 67 + 16P
We are given that (1P03)base 4 is equal to 115 in base 10. Substituting this value into the equation:
67 + 16P = 115
Now, we can solve for P:
Subtract 67 from both sides:
16P = 115 - 67
16P = 48
Divide both sides by 16:
P = 48 / 16
P = 3
Therefore, P = 3.