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An 8 bit byte can count from 0 (00000000) to 255 (11111111).
In this case all the numbers are positive integers.
If you want to use negative numbers, as well as positive, we need some way to signify a negative number.
This is done using the most significant bit. ie 1xxxxxxx is a negative number, and 0xxxxxxx is a positive number.
To create a negative number, you just take the 2's complement of the positive number.
To create the 2's complement:
step 1, invert all the bits (creating the 1's complement)
step 2, add 1. (creating the 2's complement)
To prove that -14 is 11110010, and it to +14 (00001110)
and you will get 00000000, and the carry bit will also be set off the most significant end of the byte.
I think that just about makes sense!
Just to add a practical element to this discussion, are there even any systems which use one's complement? Aren't all computer systems used today based on two's complement?
Just read the summary of the two systems in my textbook: one's complement is clumsy because it has two values for zero (0 and FF for an 8-bit number).
Only con for two's complement is that there is one more negative number than positive (-80H vs +7FH).
Just to add a practical element to this discussion, are there even any systems which use one's complement? Aren't all computer systems used today based on two's complement?
Just read the summary of the two systems in my textbook: one's complement is clumsy because it has two values for zero (0 and FF for an 8-bit number). Only con for two's complement is that there is one more negative number than positive (-80H vs +7FH).
FF = 1111 1111 = 255
How can you say that "1111 1111" would equate to zero?