Question

Convert 1011110110011100 to One half-precision (16 bit) floating

point value as a decimal value, showing all steps.

Answer 1

To convert the binary number 1011110110011100 to a 16-bit floating point value, we need to understand the IEEE 754 standard for floating point representation. By analyzing the given binary number, we can represent it in scientific notation and convert it to a 16-bit floating point value. The final decimal equivalent is approximately 2,001.06.

Step-by-step explanation:

To convert the binary number 1011110110011100 to a 16-bit floating point value, we need to understand the IEEE 754 standard for floating point representation.

In a 16-bit floating point representation, the format consists of 1 bit for the sign, 5 bits for the exponent, and 10 bits for the significand (mantissa).

By analyzing the given binary number, we can represent it in scientific notation as follows: 1.011110110011100 x 2^13

The sign bit is 0 (since it is a positive number), the exponent is 13 + 15 (bias), and the significand is 0111101100 (with a hidden bit of 1). Thus, the final 16-bit floating point value is 0 10000111 0111101100.

In decimal form, this floating point number is approximately equal to 2,001.06.