Question

The negative decimal (base 10) integer value of -27 is represented in 8-bit 2's complement as:

11100101

10011011

00011011

11100100

Answer 1

2's complement binary number notation
--------------------------------------------------
0111    1111     =   +127 decimal
......
0000 0010   =       +2 decimal
0000 0001    =       +1 decimal
0000 0000    =        0 decimal
1111      1111     =       -1 decimal
1111      1110    =       -2 decimal
......
1000 0001     =    -127 decimal
1000 0000     =   -128 decimal

Just for fun, try adding (in binary) +1 to -1, then +2 to -2, and +127 to -127
and note that the sums are zero (with a carry-out bit). This should
satisfy you that the negative numbers really make sense. Note that there is not a representation for +128 even though there is one for -128. Just for fun, try adding (in binary) -1 to -127 to see that you really do get -128. Then see what happens when you add (in binary) +1 to +127 to try to see +128.