When a message was re-encoded from an 8-bit code to a 16-bit UNICODE encoding, its size increased by 2048 bytes.

When a message was re-encoded from an 8-bit code to a 16-bit UNICODE encoding, its size increased by 2048 bytes. What was the information volume of the message (in bytes) before re-encoding?

Let’s denote the number of characters in the message by X.
To work with data of uniform dimension, let’s convert bits to bytes:
8 bits = 1 byte;
16 bits = 2 bytes.
Let’s compose an equation according to the condition of the problem:
X * 1 byte = X * 2 bytes – 2048 bytes.
Let’s solve the resulting equation:
X + 2048 = 2X;
2X – X = 2048;
X = 2048.
The text consists of 2048 characters. Before recoding, 1 character took 8 bits (1 byte) of memory, therefore, the entire text occupied 2048 * 1 = 2048 bytes = 2 KB (1 KB = 1024 bytes).
Answer: 2048 bytes.