Why write 1,000,000,000 as 1000*1000*1000 in C?

One reason to declare constants in a multiplicative way is to improve readability, while the run-time performance is not affected. Also, to indicate that the writer was thinking in a multiplicative manner about the number.

Consider this:

double memoryBytes = 1024 * 1024 * 1024;

It's clearly better than:

double memoryBytes = 1073741824;

as the latter doesn't look, at first glance, the third power of 1024.

As Amin Negm-Awad mentioned, the ^ operator is the binary XOR. Many languages lack the built-in, compile-time exponentiation operator, hence the multiplication.

Why not 1000^3?

The result of 1000^3 is 1003. ^ is the bit-XOR operator.

Even it does not deal with the Q itself, I add a clarification. x^y does not always evaluate to x+y as it does in the questioner's example. You have to xor every bit. In the case of the example:

1111101000₂ (1000₁₀)
0000000011₂ (3₁₀)
1111101011₂ (1003₁₀)

But

1111101001₂ (1001₁₀)
0000000011₂ (3₁₀)
1111101010₂ (1002₁₀)