Question

Write the equivalent decimal value of the given 2's complement number (101101110011110.1)2.

Answer 1

20220222022220. 2 is the answer

Answer 2

Answer:

$(101101110011110.1)_2=(23454.5)_{10}$

Step-by-step explanation:

To find : Write the equivalent decimal value of the given 2's complement number $(101101110011110.1)_2$ ?

Solution :

The given number is in the binary form.

We have to convert binary into a decimal number by multiplying the place place to 2 the power.

$(101101110011110.1)_2$ can be written as base 10,

$=(1\times2^{14}+0\times2^{13}+1\times2^{12}+1\times2^{11}+0\times 2^{10}+1\times2^9+1\times2^8+1\times2^7+0\times2^6+0\times2^5+1\times2^4+1\times2^3+1\times2^2+1\times2^1+0\times2^0)+(1\times2^{-1})$

$=(16384+0+4096+2048+0+512+256+128+0+0+16+8+4+2+0)+(0.5)$

$=23454+0.5$

$=23454.5$

Therefore, $(101101110011110.1)_2=(23454.5)_{10}$