Solution

The correct answer is 1100.0100

Key PointsFixed point representation is a way of storing real numbers in binary form. A 4 + 4 binary fixed point accommodates 4 bits for the integer part (one of them being the sign bit) and 4 bits for the fractional part.

EXPLANATION:

Here is how we work out the binary equivalent of -3.72:

• Integer part (-3):
  • The binary representation of 3 is 0011.
  • In the 2's complement system (which is used to represent negatives), flip the bits (1100) and then add 1 to get the representation of -3 which gives us 1101.
  • Since we are representing a 4-bit binary number, we need to consider only 4 bits which is 1100 after discarding overflow bits. Why do we do that? While overflow is generally considered an error, in 2's complement binary arithmetic, an overflow is silently ignored.
  • So the binary representation of -3 is 1100.
• Fraction part (0.72): For the fractional part, we keep multiplying by 2:
  • 0.72 * 2 = 1.44 => the first digit after decimal point is 1.
  • 0.44 * 2 = 0.88 => the second digit after decimal point is 0.
  • 0.88 * 2 = 1.76 => the third digit after decimal point is 1.
  • 0.76 * 2 = 1.52 => the fourth digit after decimal point is 1. Therefore, the binary equivalent of 0.72 in 4-bit precision is .0100.

So the binary fixed point equivalent of -3.72 is -3 for the integer part, and 0.72 for the fractional part, combine them and we get answer: 1100.0100