This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back IT — missed you this week. b) i) Show how this number can be normalized. Step 1: Separate the mantissa and exponent. The given floating-point binary number is 11101011. It is stored using 5 bits for the mantissa and 3 bits for the exponent. Mantissa: 11101_2 Exponent: 011_2 Step 2: Convert the mantissa to its denary (decimal) equivalent. The mantissa 11101_2 is in 2's complement form. The binary point is assumed after the first bit (sign bit). So, the mantissa is 1.1101_2. Since the MSB is 1, it's a negative number. Value = -1 · 2^0 + 1 · 2^-1 + 1 · 2^-2 + 0 · 2^-3 + 1 · 2^-4 Value = -1 + 0.5 + 0.25 + 0 + 0.0625 = -1 + 0.8125 = -0.1875_10. Step 3: Convert the exponent to its denary equivalent. The exponent 011_2 is in 2's complement form.