Final answer:
To solve for x in hexadecimal, add 2BC to both sides, convert all terms, perform the addition, then convert the result back to hexadecimal where x equals 319 base 16.
Step-by-step explanation:
To solve the equation x base 16 - 2bc base 16 = 5d base 16 for x, we need to perform arithmetic in hexadecimal (base 16). Hexadecimal numbers include the digits 0-9 and the letters A-F, where A is equivalent to 10 in decimal, B to 11, C to 12, and so on up to F which is 15.
First, we write the equation properly, converting all letters to their decimal equivalents:
(1) x - (2×16² + 11×16 + 12) = 5×16 + 13
Solve for x by adding 2BC to both sides of the equation:
(2) x = 5×16 + 13 + (2×16² + 11×16 + 12)
Calculate the sum on the right side of the equation:
(3) x = (5×16 + 13) + (2×16² + 11×16 + 12)
(4) x = (80 + 13) + (512 + 176 + 12)
(5) x = 93 + 700
The result is 793 in decimal, which we need to convert back to hexadecimal. We do this by dividing 793 by 16 repeatedly and tracking the remainders:
- 793 / 16 = 49 remainder 9 (9 in hex)
- 49 / 16 = 3 remainder 1 (1 in hex)
- 3 / 16 = 0 remainder 3 (3 in hex)
Reading the remainders backwards gives us 319 base 16.
So, the solution is x = 319 base 16.