How do you convert to 47.625 convert to 16 bit floating point number representation?

Answer 1

To convert the decimal number 47.625 to 16-bit floating point representation (following the IEEE 754 standard), we first express it in binary. The integer part (47) is 101111, and the fractional part (.625) is .101. Combining these gives us 101111.101. This is normalized to 1.011111 × 2^5. The exponent (5) is stored with a bias of 15, resulting in an exponent of 20 (or 10100 in binary). The final 16-bit representation consists of 1 sign bit (0 for positive), 5 bits for the exponent (10100), and 10 bits for the mantissa (0111110000), yielding: 0 10100 0111110000.