To convert the binary number 11101.012 to decimal, we will calculate the position value for each binary digit and then sum these values.

  1. First, we write the position values above each digit. The table below shows the position values in powers of 2 and decimal.
Position
Values
24 23 22 21 20   2-1 2-2
16 8 4 2 1   0.5 0.25
Binary Digits 1 1 1 0 1 . 0 1
  1. Note that 20 is located to the immediate left of the radix point. As we move to the left, the power of the position value increases by 1 for each digit, and as we move to the right the power of the position value decreases by 1 for each digit.

  1. For each column, we multiply the position value of the column by the digit contained in that column. Since any number multiplied by zero equals zero, we ignore the columns with the digit '0'. The remaining columns all contain '1's, so we can simply record their position values below.
Position Value 16 8 4 2 1   0.5 0.25
Binary Digit 1 1 1 0 1 . 0 1
Product 16 8 4 0 1   0 0.25
  1. Finally, we sum the values we listed to get the decimal answer.

11101.012 = 16 + 8 + 4 + 1 + 0.25 = 29.25

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