By Miles Murdocca
Our target in penning this ebook is to reveal the internal workings of the trendy electronic computing device at a degree that demystifies what is going on contained in the desktop. the one prerequisite to rules of laptop structure is a operating wisdom of a high-level programming language. The breadth of fabric has been selected to hide subject matters commonly present in a primary direction in machine structure or laptop association. The breadth and intensity of assurance were urged to put the start scholar on a high-quality music for carrying on with reports in computer-related disciplines. In making a machine structure textbook, the technical matters fall into position particularly clearly, and it's the organizational concerns that convey very important gains to fruition. a few of the positive aspects that acquired the best cognizance in ideas of laptop structure contain the alternative of the guideline set structure (ISA), using case reviews, and a voluminous use of examples and workouts.
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011)2. Non Terminating Fractions Although this method of conversion will work among all bases, some precision can be lost in the process. For example, not all terminating base 10 fractions have a terminating base 2 form. 2)10 to base 2 as shown in Figure 2-3. 2 reappears, and the process repeats ad infinitum. As to why this can happen, consider that any non-repeating base 2 fraction can be represented as i/2k for some integers i and k. ) Algebraically, i/2k = i×5k/(2k×5k) = i×5k/10k = j/10k 1. Alternatively, we can use the base 10 number system and also avoid the conversion if we retain a base 2 representation, in which combinations of 1’s and 0’s represent the base 10 digits.
Two binary numbers A and B are added from right to left, creating a sum and a carry in each bit position. Since the rightmost bits of A and B can each assume one of two values, four cases must be considered: 0 + 0, 0 + 1, 1 + 0, and 1 + 1, with a carry of 0, as shown in the figure. The carry into the rightmost bit position defaults to 0. For the remaining bit positions, the carry into the position can be 0 31 32 CHAPTER 2 DATA REPRESENTATION Carry in Operands 0 0 + 0 0 0 + 1 0 1 + 0 0 1 + 1 1 0 + 0 1 0 + 1 1 1 + 0 1 1 + 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 Carry Sum out Example: Carry Addend: A Augend: B Sum Figure 2-5 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 + 0 1 0 1 1 0 1 0 (124)10 (90)10 1 1 0 1 0 1 1 0 (214)10 Example of binary addition.
We will see that the IEEE 754 floating point format uses a hidden bit. 3 REPRESENTING FLOATING POINT NUMBERS IN THE COMPUTER—PRELIMINARIES Let us design a simple floating point format to illustrate the important factors in representing floating point numbers on the computer. Our format may at first seem to be unnecessarily complex. We will represent the significand in signed magnitude format, with a single bit for the sign bit, and three hexadecimal digits for the magnitude. The exponent will be a 3-bit excess-4 number, with a radix of 16.