Binary Numbers
Created: November 18, 2018 by [lek-tin]
Last updated: November 18, 2018
For a 8-bit number, there are two ways to represent number:
unsigned values 0 to 255
signed values range from -128 (-2^8 = 10000000) to 127 (2^8 - 1)
signed -128 = 10000000
signed -127 = 10000001
signed -1 = 11111111
signed 0 = 00000000
signed 127 = 01111111
signed 127 + (-127) = 10000001 + 01111111 = 0
If a number is assigned with value that is too big for it to hold, overflowing would happen,
2^32 = 4,294,967,296 is the largest unsigned 32 bit value. He’s however using signed values, their maximum is 2^31-1 = 2,147,483,647, when you exceed that with for example 10,000,000,000, then it will go to the smallest possible value (-2^31) and count on from there.
This is what happens:
0 -> 2^31-1 (10,000,000,000 - 2^31-1 = 7,852,516,353 remaining) => overflow -2^31 -> 2^31-1 (7,852,516,353 - (2^31-1 + 2^31) = 3,557,549,056 remaining) => overflow -2^31 -> 1410065408 (3,557,549,056 - (2^31 + 1410065408) = 0 remaining)