To determine the single-precision floating-point representation on a 32-bit word-length computer for the given decimal numbers, we need to convert them into binary and then apply the IEEE 754 standard for single precision. a. 2-30: The decimal number 2-30 is a very small positive number. In single precision, it would be represented as follows: Determine the sign bit: Since the number is positive, the sign bit is 0. Convert the number into binary scientific notation: 230 = 22228. Determine the exponent: The exponent is bias 127 + (-30) = 97, which in binary is 01100001. Normalize the mantissa: The normalized mantissa is 1.0. Putting it all together, the representation of 2-30 in single precision is: 0 01100001 000000000000000000000000000 b.…show more content… In single precision, it would be represented as follows: Determine the sign bit: Since the number is positive, the sign bit is 0. Convert the integer part and fractional part into binary: Integer part: 64 = 1000000 Fractional part: 0.015625 = 0.000001 Combine the integer and fractional parts: 64.015625 = 1000000.000001 Determine the exponent: Since the number is 26 with no shifting of the decimal point, the exponent is 6. Bias 127 + 6 = 133, which in binary is 10000101. Normalize the mantissa: The normalized mantissa is 1.000001. Putting it all together, the representation of 64.015625 in single precision is: 0 10000101 00000000010000000000000 c. -8 224: The decimal number -8 224 is a negative number. In single precision, it would be represented as follows: Determine the sign bit: Since the number is negative, the sign bit is 1. Convert -8 into binary: -8 in binary is 1000. Determine the exponent: Since the number is 224 with no shift of the decimal point, the exponent is
