(Solved):   (a) Determine the 4-bit Binary representation of the following number with a minimum round ...

 

(a) Determine the 4-bit Binary representation of the following number with a minimum round-off error. \( 0.9160_{10} \) 4-bit Binary representation of \( 0.9160_{10} \) The binary representation \( 0.1110 \) actually represents: \[ 1 \times 2^{-1}+1 \times 2^{-2}+1 \times 2^{-3}+0 \times 2^{-4}=0.5+0.25+0.125=0.875 \] The binary representation \( 0.1111 \) actually represents: \[ \begin{array}{c} 1 \times 2^{-1}+1 \times 2^{-2}+1 \times 2^{-3}+1 \times 2^{-4}=0.5+0.25+0.125+0.0625=0.9375 \\ 0.1110 \rightarrow \text { Round-off error }=(0.9160-0.875) / 0.9160=4.475 \% \\ 0.1111 \rightarrow \text { Round-off error }=(0.9375-0.9160) / 0.9160=2.347 \% \end{array} \]