Question

what decimal number does the bit pattern 0�0c000000 represent if it is a fl oating point number? use the ieee 754 standard

Answer 1

The decimal number represented by the bit pattern 0�0c000000 in IEEE 754 floating point format is 0.0.

In the IEEE 754 standard, the bit pattern 0�0c000000 represents the value 0.0 when interpreted as a floating point number.

Step-by-step explanation:

In IEEE 754 floating point representation, the format comprises a sign bit, exponent bits, and fraction bits. The given bit pattern '0�0c000000' seems to indicate a sign bit of 0, an exponent of all zeros, and a fraction part consisting entirely of zeros.

The sign bit indicates the sign of the number, where '0' typically represents a positive value. The exponent bits being all zeros suggest a biased exponent value of 0.

In the IEEE 754 standard, when the exponent is set to zero, the number is considered a denormalized value. For such numbers, the fraction bits alone determine the actual value.

A floating point number is computed using the formula:
`(-1)^sign` * 1.fraction *
`2^(^exponent ^- ^bias^`). In this case, the exponent being 0 implies a bias of -126 for single precision floating point numbers.

With all fraction bits being zero, the value represented is 0.0, as per the IEEE 754 standard.

Answer 2

The decimal number represented by the bit pattern 0b0c000000 in IEEE 754 floating-point format is 0.

Step-by-step explanation:

In the IEEE 754 floating-point standard, the bit pattern consists of three components: the sign bit, the exponent, and the fraction (also known as the significand or mantissa). For the given bit pattern 0b0c000000, "0" is the sign bit, "c000000" represents the exponent, and the fraction is implied by the leading "1" in normalized binary representation. In this case, the exponent is zero, and the fraction is also zero. According to IEEE 754, when the exponent is zero, the value is a special case known as "denormalized" or "subnormal," and the number represented is zero.