Convert the following into Binary with Floating-Point representation. (If the conversion is infinite, please stop according to floating point convention of half word) The bias for 16 bits is 15

Question

1. 8
2. -9.25

Answer 1

For 8:

Normalization: 8 can be written as 1.0000000 * 2^3.

Binary conversion: The mantissa 1.0000000 is represented in binary as 1.0000000.

Encoding: The sign bit for positive numbers is 0. The exponent for 2^3 is 3 + 15 = 18, which is represented in binary as 10010. The mantissa 1.0000000 is represented as 7 bits in binary, so the final representation is 0 10010 000 0111 11000.

For -9.25:

Normalization: -9.25 can be written as -1.1101000 * 2^3.

Binary conversion: The mantissa -1.1101000 is represented in binary as -1.1101000.

Encoding: The sign bit for negative numbers is 1. The exponent for 2^3 is 3 + 15 = 18, which is represented in binary as 10010. The mantissa -1.1101000 is represented as 7 bits in binary, so the final representation is 1 10010 011 1010 11000.