Question

what is the equivalent 2s complement representation for -15 in 16 bit hexadecimal representation​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

PROCESS

STEP 1 : Take the given negative value

STEP 2 : Make it positive

STEP 3 : Convert it into 16 bit Binary Value

STEP 4 : Negate the value

STEP 5 : Add 1 to the obtained value

STEP : 6 Convert it in Hexadecimal

TO REMEMBER

In Hexadecimal

A = 10 , B = 11 , C =12 , D= 13 , E = 14 , F= 15

TO DETERMINE

The equivalent 2s complement representation for -15 in 16 bit hexadecimal representation

EVALUATION

STEP 1 : The given value is - 15

STEP 2 : Positive value of - 15 is 15

STEP 3 :

$15 = 2 \times 7 + 1$

$7 = 2 \times 3 + 1$

$3 = 2 \times 1 + 1$

$1 = 2 \times0 + 1$

In 16 bit Binary Value 15 can be written as

$\sf{ 0000 \: \: 0000 \: \: 0000 \: \: 1111\: }$

STEP 4 : Negating

$\sf{ 0000 \: \: 0000 \: \: 0000 \: \: 1111\: } \: \: we \: get$

$\sf{ \red{ 1111} \: \: \green{ 1111} \: \: \pink{1111} \: \: 0000\: }$

STEP 5 : Adding 1 to the obtained value

$\sf{ \red{ 1111} \: \: \green{ 1111} \: \: \pink{1111} \: \: 0000\: } \: we \: get$

$\sf{ \red{ 1111} \: \: \green{ 1111} \: \: \pink{1111} \: \: 0001\: }$

STEP : 6 Convert it in Hexadecimal we get

$\sf{ \red{ | 1 \times {2}^{3} + 1 \times {2}^{2} + 1 \times {2}^{1 } + 1 \times {2}^{0} | } \: \: \green{ | 1 \times {2}^{3} + 1 \times {2}^{2} + 1 \times {2}^{1 } + 1 \times {2}^{0} |} \: \: \pink{| 1 \times {2}^{3} + 1 \times {2}^{2} + 1 \times {2}^{1 } + 1 \times {2}^{0} |} \: \: | 0 \times {2}^{3} + 0 \times {2}^{2} + 0 \times {2}^{1 } + 1 \times {2}^{0} |\: }$

$= \sf{ \red{ | 15 \: | } \: \: \green{ | 15 |} \: \: \pink{| 15 |} \: \: | 1 |\: }$

$= \sf{ FFF1\: }$

RESULT

SO the required answer is

$\boxed{ \sf{ \:FFF1 \: }}$