1. **State the problem:** Convert the 16-bit floating-point number 01101110 00000100 to its decimal (denary) value. 2. **Understand the format:** The first 8 bits (01101110) represent the mantissa in two's complement. The next 8 bits (00000100) represent the exponent in two's complement. 3. **Convert mantissa from two's complement:** - Mantissa bits: 01101110 - Since the leftmost bit is 0, the number is positive. - Convert binary 01101110 to decimal: $$0\times2^7 + 1\times2^6 + 1\times2^5 + 0\times2^4 + 1\times2^3 + 1\times2^2 + 1\times2^1 + 0\times2^0 = 0 + 64 + 32 + 0 + 8 + 4 + 2 + 0 = 110$$ - Mantissa = 110 4. **Convert exponent from two's complement:** - Exponent bits: 00000100 - Leftmost bit is 0, so positive number. - Convert binary 00000100 to decimal: $$0\times2^7 + 0\times2^6 + 0\times2^5 + 0\times2^4 + 0\times2^3 + 1\times2^2 + 0\times2^1 + 0\times2^0 = 0 + 0 + 0 + 0 + 0 + 4 + 0 + 0 = 4$$ - Exponent = 4 5. **Calculate the floating-point value:** - Formula: $$\text{value} = \text{mantissa} \times 2^{\text{exponent}}$$ - Substitute values: $$110 \times 2^4 = 110 \times 16 = 1760$$ 6. **Final answer:** The decimal value of the floating-point number 01101110 00000100 is **1760**.