Question

Convert the following unsigned binary number to unsigned decimal. 110011.101

Answer 1

Answer:

51.625

Step-by-step explanation:

Given a unsigned binary number, to calculate the unsigned decimal:

first, starting at dot, you list the positive powers of 2 from right to left beginning in $2^{0}$  that is equal to “1”.  Increase by one the exponent in every power until you complete the total quantity of digits from the unsigned binary number. In this case, since dot to the left, the binary number has six digits (110011). That is to say that you get the followings powers: $2^{5}$  $2^{4}$  $2^{3}$ $2^{2}$  $2^{1}$  $2^{0}$.

Second, do the same from dot to the right but this time, you list the negative powers of 2 from left to right beginning in $2^{-1}$ that is equal $\frac{1}{2}$ = 0.5. so you get:    $2^{-1}$  $2^{-2}$  $2^{-3}$

Now, join two parts and you get:

$2^{5}$      $2^{4}$     $2^{3}$      $2^{2}$      $2^{1}$       $2^{0}$    $2^{-1}$      $2^{-2}$      $2^{-3}$

1        1       0       0       1       1.        1        0        1

Then, you write the equivalent of each of the power below from corresponding binary digit, like that:

$2^{5}$      $2^{4}$     $2^{3}$      $2^{2}$      $2^{1}$       $2^{0}$    $2^{-1}$      $2^{-2}$      $2^{-3}$

1        1       0       0       1       1.        1        0        1

|         |        |         |        |        |         |         |         |  

32    16      8       4       2       1       0.5   0.25   0.125  

Finally, you write under the line the equivalent of each power that corresponding to “1” and write “0” under the line, the one that corresponding to “0”, and you sum each one of finals values. Like that:

$2^{5}$      $2^{4}$     $2^{3}$      $2^{2}$      $2^{1}$       $2^{0}$    $2^{-1}$      $2^{-2}$      $2^{-3}$

1        1       0       0       1       1.        1        0        1

|         |        |         |        |        |         |         |         |  

32    16      8       4       2       1       0.5   0.25   0.125  

_______________________________________  

32    16      0       0       2       1       0.5     0      0.125  

32 + 16 + 0 + 0 + 2 + 1 + 0.5+ 0 + 0.125 = 51.625

So that the equivalent from unsigned binary number 110011.101 to unsigned decimal is 51.625