Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof / 5 / d / Solution

For the unsigned interpretation of the binary string, the set positions have weights $2^{15},2^{13},2^{12},2^{11},2^{10},2^8,2^6,2^5,2^4$. ThusIn 16-bit two's complement, the most significant bit is set, so subtract $2^{16}$ from that unsigned interpretation:For a half-precision floating-point number, split the fields at their actual boundaries rather than the printed groups of four:The sign is negative, the true exponent is $15-15=0$, and the fraction is $2^{-2}+2^{-4}+2^{-5}+2^{-6}=23/64$. It is a normal finite value, so