Siemens Level 1 Practice Exam

To find the decimal equivalent of the floating point binary number 1011 1101.0110, we first need to break it down into two parts: the integer part (before the binary point) and the fractional part (after the binary point).

Starting with the integer part, 1011 1101 in binary translates to:

- 1 × 2^7 = 128

- 0 × 2^6 = 0

- 1 × 2^5 = 32

- 1 × 2^4 = 16

- 1 × 2^3 = 8

- 0 × 2^2 = 0

- 1 × 2^1 = 2

- 1 × 2^0 = 1

Adding these values together gives:

128 + 0 + 32 + 16 + 8 + 0 + 2 + 1 = 187

Now, moving on to the fractional part, .0110 in binary translates to:

- 0 × 2^-1 = 0

- 1 × 2^-2 = 0.25

- 1 × 2^-3 = 0