Convert the following from binary to decimal SHOW YOUR WORK

Convert the following from binary to decimal – SHOW YOUR WORK! 11000000111001.00111

Step by step process is

1) write down the binary number and list the power of 2 from right to left starting from 2^0.

2) write the digits of binary number to the corresponding powers of two.

3) Sum up the powers of two.

4) When we assign 2 powers to the digits after decimal point then assign negative powers.

11000000111001.00111

First are left to the decimal points

1*2^13 + 1*2^12 +0* 2^11 + 0*2^10 +0* 2^9 + 0*2^8 +0*2^7 +0*2^6 +1*2^5+ 1*2^4 +1* 2^3+0*2^2+0*2^1+1*2^0

Now right to decimal points

0*2^-1+ 0*2^-2+ 1*2^-3+ 1*2^4 +12^-5

Now get the values and sum up

1) 1*2^13 + 1*2^12 +0* 2^11 + 0*2^10 +0* 2^9 + 0*2^8 +0*2^7 +0*2^6 +1*2^5+ 1*2^4 +1* 2^3+0*2^2+0*2^1+1*2^0

1*8192 + 1*4096 + 0 +0 +0+0+0+0 +32+16+8+0+0+1 = 12330

2) 0*2^-1+ 0*2^-2+ 1*2^-3+ 1*2^4 +1*2^-5

0+0+0.125+0.0625+0.03125 = 0.21875

So decimal conversion of given binary is 12330.21875