Digital Electronics - Number Systems and Codes - Discussion

1001.0010.

1001 = 1*2^3 + 0*2^2 + 0*2^1 + 1*2^0 = 8 + 0 + 0 + 1 = 9
.0010 = 0*2^-1 + 0*2^-2 + 1*2^-3 + 0*2^-4 = 0 + 0 + (-8) + 0 = -8 = 1/8 = 0.25.
9.25 ans.

1001.0010 (base 2) is given. it should be converted into decimal (base 10).

Step1: From before the decimal point, start multiplying the bit '1' (as per the given question) with 2^0.

Step2: Similarly multiply each digit, moving towards left with 2^1 , 2^2,......... (positive powers) and add them all.

Step 3: Similarly multiply each digit, moving towards right with 2^(-1) , 2^(-2)......... (negative powers) and add them all.

Here: 1 * 2^(3) + 0 * 2^(2) + 0 * 2^(1) + 1 * 2^(0) . 0 * 2^(-1) + 0 * 2^(-2) + 1 * 2^(-3) + 0 * 2^(-4) = 9.125 (as 2^(-3) = 1/ 2^(3) = 1/8 = 0.125).

1001.0010 = (1*2^3)+(0*2^2)+(0*2^1)+(1*2^0)+(0*2^-1)+(0*2^-2)+(1*2^-3)+(0*2^-4) = 9.125.

Agree, 9.125 is the right answer.

Really I can't understand this, please explain easily.

Thanks everyone for explaining the answer.

Can't understand the logic of the question. Please explain it for me.

I didn't understand it. Please help me.

How 9.125? Please explain the solution clearly.

1001=9 after point
.0010=0*2^0+0*2^1+1*2^3+0*2^4=.125