What decimal number does the bit pattern 0x0C000000 represent if it is a floating point number? Use the IEEE 754 standard.

The bit pattern 0x0C000000 represents a floating point number in hexadecimal format.

To convert it to decimal using the IEEE 754 standard, we need to break down the bits into their respective parts:

1. The first bit is the sign bit, with a value of 0, indicating that the number is positive.
2. The next 8 bits represent the exponent, which is biased by 127. In this case, the exponent bits are 0xC0, which is equal to 192 in decimal. Subtracting the bias of 127 gives us an actual exponent of 65.
3. The remaining 23 bits represent the significand or mantissa, with an implied leading 1. In this case, the significand bits are 0x000000, which means the actual significand is 1.

Putting it all together, we get:

(-1)^0 * 1 * 2^(65-127) = 2^(-62) = 0.0000000000000000000000000000000000000000000000000000000015625

Therefore, the decimal number represented by the bit pattern 0x0C000000 in IEEE 754 floating point format is approximately 0.0000000000000000000000000000000000000000000000000000000015625.