An 8-bit two's-complement Q4.4 format uses four bits to the left of the binary point…

An 8-bit two's-complement Q4.4 format uses four bits to the left of the binary point, including the sign bit, and four bits to the right. The encoded value is the 8-bit two's-complement integer formed by the eight bits, multiplied by \(2^{-4}\). State the representable range as a closed interval of multiples of \(2^{-4}\). Encode \(-3.375\) and \(+2.75\). Decode \(1011.0100_{2}\) and \(1111.1111_{2}\). Add the Q4.4 patterns \(0010.1100_{2}\) and \(1101.1010_{2}\) as 8-bit two's-complement strings, and give both the 8-bit sum pattern and the decimal value it represents in Q4.4. State whether that addition overflows Q4.4.

Q4.4 is 8-bit two's complement with an implied binary point in the middle, so every value is \(k/16\) for an 8-bit two's-complement integer \(k\).