Question

What is the largest positive number that can be represented with 12 bits in 2's complement representation? Answer in hexadecimal. Include the Ox, but do not include spaces in your answer

Answer 1

The largest positive number that can be represented with n bits in 2s complement representation is  2^N−1 − 1.

with 12 bits the largest number would be 2^11 - 1 = 2047

so 2047 in hexadecimal 7FF

The answer is 0x7FF

Answer 2

ANSWER :

Largest 12 bit 2’s 

= 111111111111 (binary)

= 2^11 + 2^10 + 2^9 + 2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 1

= 4095 

4095 in hexadecimal system :

4095/16 = Q 255 R 15 , take 15 I.e F to unit place.

255/16 = Q15 R 15 , take 15 I.e F  to 2nd place (to the left of first place)

15/16 + Q0 R 15 , take 15 I.e. F to 3rd place (to the left of 2nd place)

Hence, 4095 (decimal) is  F F F in hexadecimal. 

So, the ANSWER is : OxFFF