Electronics - Number Systems and Codes - Discussion

Given (1001.0010)

To convert into a decimal number we need to multiply each binary digit with 2. As we move towards the left part of the decimal number the power of the 2 increases i.e; ( 2^0, 2^1, 2^2, 2^3......) as we move towards the right part of the decimal the power of 2 decreases i.e;( 2^-1, 2^-2, 2^-3)

So after multipying the binary digits with the number 2 we get 9.125.

In Detail: Given (1001.0010) , multiply each binary digit with 2 along with their powers. i.e;
2^3x1 + 2^2x0 +2^1x0 + 2^0x1 + 2^-1x0 + 2^-2x0 + 2^-3x1 +2^-4x0.
= 8 + 0 + 0 + 1 + 0 + 0 + 0.125 + 0 => 9.125.

Answer = D

1001.0010 Assume like this;

3 2 1 0.-1 -2 -3 -4 as powers of the given number. And the given conversation is about binary so we have to use 2 as a base. Where 1 is there base is present and for 0 base 2 is absent.
2^3 + 0 + 0 + 2^0. 0 + 0 + 2^-3 + 0.
= 8 + 1.125,
= 9.125.

2^3+0+0+1 = 9;
2^(-1)*0 + 2^(-2)*0 + 2^(-3)*1 + 2^(-4)*0 = 1/8 = 0.125.

2^3+0+0+1=9; and
0+0+2^(-3)= .125

So ans is 9.125

How to solve this equation? Please Explain.

Please explain in detail can't understand.

Can anyone please explain in detail?

Can someone explain in detail?