Final answer:
After converting the hexadecimal number 0C000000 to the IEEE 754 format, the resulting decimal number is very small, approximately expressed as 2.9 × 10^-35 using scientific notation.
Step-by-step explanation:
Converting Hexadecimal to Decimal using IEEE 754 Single Precision Format
To convert the hexadecimal number 0C000000 to decimal using the IEEE 754 single precision format, we need to understand the structure of an IEEE 754 floating point number. This structure is composed of a sign bit, an 8-bit exponent, and a 23-bit significand (mantissa). The hexadecimal number 0C000000 first needs to be converted into binary, resulting in 00001100 00000000 00000000 00000000. In binary, this corresponds to a sign bit of 0 (positive), an exponent of 00001100, and a significand of 00000000000000000000000.
The exponent is biased in the IEEE 754 format. The bias for single precision is 127 (27 - 1). The actual exponent is calculated by subtracting this bias from the binary exponent. Here, the binary exponent of 00001100 (12 in decimal) gives us an actual exponent of -115 after subtracting the bias (12 - 127 = -115). The significand is expressed as 1 plus the binary fraction represented by the 23 binary digits after the leading bit, which is 0 for this number. Thus, our significand is 1.0 because there are no significant digits after the leading bit in the significand.
Now, let's put these pieces together. The number in decimal is -1sign × significand × 2exponent, which for our example is 1 × 1.0 × 2-115. Since the exponent is -115, which is a very small power of 2, the resulting number is very small as well. In standard decimal form, it would have 34 leading zeros after the decimal point. Since the number is too small to represent normally in decimal form, we often use scientific notation to express it as approximately 2.9 × 10-35.