First, what is a 4-bit signed binary system?
It's a way to represent numbers, like many other systems. But the way this differs is that the leftmost bit is typically used as the sign bit, 0 negative 1 positive. The remaining bits are used to represent the magnitude of the number.
Lets give some examples.
The binary number 0001 represents 1 in decimal.
The binary number 0010 represents 2 in decimal.
The binary number 0011 represents 3 in decimal.
The binary number 0100 represents 4 in decimal
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Why does this pattern exist? In 4-bit signed binary, each place value represents 1 until added.
0010 is one more than 0001, so it is 2 in decimal.
You might think 0100 should be 3, but because this is a binary system, we can now do 0011 to be 3. 0100 is actually 4.
Coding is all about optimizing what you have, so you use every combination to represent more things.
The negative side is similar.
1000 also adds to 0, but it is negative. This computes to -0.
The binary number 1001 represents -1 in decimal.
The binary number 1011 represents -2 in decimal.
*Note: Most computers convert this to just 0 also.