Mock Exam Question

I need help understanding this code.
I know that the highest number a byte can be is 127, but I don't see the connection:
(byte)128 = -128
(byte)255 = -1
(byte)256 = 0
Thank you for any responses
class E2 {
static byte a = (byte)127;
static byte b = (byte)128;
static byte c = (byte)255;
static byte d = (byte)256;
public static void main(String args[]) {
System.out.print(a + " " + b + " " + c + " " + d);
}
}
/*
127 -128 -1 0
*/

This campfire story might be helpful.

Thank you for the response and posting great mock exams. I am learning a lot about Java from your site.
I have read that campfire story and I enjoyed it very much. I wish there was for 3D arrays.
I am assuming that the probelm that I posted above:
when the amount exceeds 2^7-1 and it automatically is forced to -1.
Thanks again

A byte occupies eight bits
+127 is represented as: 0111 1111
The first digit is a sign, 0 is positive in this case. If the left first digit was a 1, the value would be negative.
128 in 32 bit binary is 0000 0000 0000 0000 0000 0000 1000 0000
when casting to a byte, the left 24 bits are discarded. The remaining is
1000 0000
This is now a byte. Because the first digit is a 1 the value is negative. Convert using two's complement. Twos complement requires inverting and adding 1.
start 1000 0000
invert 0111 1111
add 1
result 1000 0000 = 128 and it was negative = -128

256 is in binary is :
0000 0000 0000 0000 0000 0001 0000 0000
cast to a byte discards the left 24 bits leaving
0000 0000 which is 0
255 is one less than 256 so it is �1
OR
0000 0000 0000 0000 0000 0000 1111 1111
cast to a byte leaves
1111 1111
The first digit is 1 so it is negative so it needs to be converted using two's complement
start 1111 1111
invert 0000 0000
add 1
result 0000 0001 and remember it is negative so it is -1

Thank you!
That helped!

Originally posted by Jacob Michaels:
I wish there was for 3D arrays.

I'm not sure I understand this statement. Given Java's Collections and Maps, it's entirely possible to store an array of Map objects in another Map object and retrieve by key.

On Dan's recommendation I too read the campfire stories. They are beautiful stories.But who is writing those beautiful,imaginative stories? I didn't find the name of the authors or am I so stupid that I missed the names?
Rattan

The credits for the campfire story are provided at the bottom of the page.