Question

The bit sequence 11110111 could represent what unsigned integer and what 2’s complement integer? TWO DIFFERENT NUMBERS.

Answer 1

1)
Converting 11110111 to decimal
11110111
=> 1x2^7+1x2^6+1x2^5+1x2^4+0x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+1x64+1x32+1x16+0x8+1x4+1x2+1x1
=> 128+64+32+16+0+4+2+1
=> 247
Answer: 247

2)
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
I. first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   11110111 is flipped to 00001000
II. Add 1 to above result
00001000 + 1 = 00001001
III. Now convert this result to decimal value
Converting 1001 to decimal
1001
=> 1x2^3+0x2^2+0x2^1+1x2^0
=> 1x8+0x4+0x2+1x1
=> 8+0+0+1
=> 9
Answer: -9