Using the 14-bit floating point representation where exponents are represented u

Question

Using the 14-bit floating point representation  where exponents are represented using excess-16, convert the following, Please show the full step,

a. 11010011011000 to decimal

b. 5.15625 to binary

Explanation / Answer

a) 1 10100 11011000 sign bit is 1(-ve) exp is 10100 => in decimal it is 20. so, power of 2 is 20-16=4, since it is excess-16 frac bits are 11011000 1 10100 11011000 in decimal is -1.11011000 * 2^4 => -11101.1000 => in decimal it is -29.5. b) 5.15625 5.15625 in normal decimal is 101.00101 => 1.0100101 * 2^2 so, sign bit is 0(+ve) exp bits are (16+2=18) => 10010 frac bits are 01001010 so, 5.15625 in excess-16 format is 0 10010 01001010

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