4. Is 32(1224) a machine number in the Marc-32? Explain. Hypothetical Computer Marc-32 Within a typical computer, numbers are represented in the way just described, but with certain restrictions placed on q and m that are imposed by the available word length. To illustrate this, we consider a hypothetical computer that we call the Marc-32. It has a word length of 32 bits (binary digits) and, therefore, is similar to many personal computers and workstations. The floating-point representation for a single-precision real number in the hypothetical 32-bit computer Marc-32 is divided into three fields as shown in Figure 2.1. The bits composing a word in the Marc-32 are allocated in the following way when representing a nonzero real number x=q2m : A nonzero real number x=q2m can be written as a left-shifted normalized binary number such that the first nonzero bit in the mantissa is just before the binary point, that is, q=(1.f)2. This bit can be assumed to be 1 and does not require storage. The mantissa is in the range 1q