Question

Each of these 8-bit bytes can be interpreted as either

a 2’s complement number or an unsigned number. Find the decimal integer

that corresponds to each interpretation.

(a) FF

(b) 53

Answer 1

a)  FF
in binary it is 11111111
since left most bit is 1. this is negative. and follow these steps below
=>  flip all the bits
    11111111 is flipped to 00000000
=>  add 1 to above result
    00000000 + 1 => 00000001
=>  convert above result to decimal
    00000001 is decimal is 1
Answer: -1

b)  53
in binary it is 01010011
since left most bit is 0. this is positive. so, directly convert this to decimal
01010011
=>  0x2^7 + 1x2^6 + 0x2^5 + 1x2^4 + 0x2^3 + 0x2^2 + 1x2^1 + 1x2^0
=>  0x128 + 1x64 + 0x32 + 1x16 + 0x8 + 0x4 + 1x2 + 1x1
=>  0 + 64 + 0 + 16 + 0 + 0 + 2 + 1
=>  83
Answer: 83