I want to convert the number -29.375 to IEEE 745 16-bit floating point format. Here is my solution:
The format of the floating point number is: 1 sign bit unbiased exponent in 4 bits plus a sign bit 10 bits for the mantissa plus the explicit 1
First, I realize that 29.375 = 29 + 3/8.
Then realize that:
29 = 16 +13 = 16 + 8 + 5 = 16 + 8 + 4 + 1
1 1101.011 = 1.1101 0110 * 2^3
This gives us:
mantissa is: 1101 011000
sign: 1
exp: 00011
Hence in 16 bits, we have: 1000111101011000
Do I have this right? I was hoping that there would be a calculator on the web that I could use but I could not find one. They were all at least 32-bits.