What is the decimal equivalent of the floating point binary number 1011 1101.0110?

What is the decimal equivalent of the floating point binary number 1011 1101.0110?

• A. 189.625
• B. 189.375
• C. 188.500
• D. 190.750

Answer: (B)

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

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