Question

Decimal value of the signed magnitude binary number (11101) is
a) +13
b)-13
c) + 23
d) - 17​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Decimal value of the signed magnitude binary number ( 11101 ) is

a) + 13

b) - 13

c) + 23

d) - 17

CONCEPT TO BE IMPLEMENTED

RULE

For signed magnitude binary number -

• The most significant bit is used as the sign bit

• If the sign bit is 0 then the number is positive

• If the sign bit is 1 then the number is negative

• The remaining bits in the number are used to represent the magnitude

EVALUATION

Here the given number is

$\sf{11101}$

For understanding the concept of sign we write it as below

$\sf{ \boxed{1}1101}$

Now the 1 within bracket is used for sign

Since it is 1 so the number is negative

Now we will calculate the value of 1101 which gives magnitude of the number

$\sf{1101}$

$= \sf{(1 \times {2}^{3}) + (1 \times {2}^{2}) + (0 \times {2}^{1} ) + (1 \times {2}^{0} ) }$

$= \sf{8 + 4 + 0 + 1}$

$\sf{ = 13}$

So the required value = - 13

FINAL ANSWER

Hence the correct option is (b) - 13

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