Encoding Information

The main memory consists of a large number of storage cells, each of which can store a binary digit, or bit, having the value 0 or 1. since a single bit represents small amount of information, a group of n-bits are used while storing or retrieving. Each group of n-bits is referred to as a word of information and n is called the word length. Word lengths in microcomputers and minicomputers range from 8 to 32 bits, and large computers usually have 32 or more bits in a word.

Accessing the main memory to store or retrieve a single word of information requires distinct names or addresses for each word location. It is customary to use the numbers from 0 to M-1 as the addresses of successive locations in a memory consisting of M words. The M addresses constitute the address space of a given computer. Using binary encoding of addresses, m bits as needed to represent all addresses where 2M = M.

In general, it is not possible determine whether a main memory location contains an instruction or an operand merely by inspecting its contents. The contents of memory locations can represent either instructions or operands; the latter may be either numbers or characters. The figures illustrates 3 possible ways in which a 32 bit word can be used to represent information :

The most straight forward way that a 32 bit pattern can use bit b31 is called the sign bit. It is 0 for positive number and 1 for negative number. The magnitude of the number is determined from bits b30 through b0 by the formula.

Magnitude = b30 x 230 + …+ b1 x 21 + b0 x 20

The range of magnitudes that can be represented in this way is from 0 to 231 –1, and the numbers are said to be in the binary positional notation. The encoding format is called the sign and magnitude representation.

In addition to number, computers must be able to handle characters. Characters can be alphabets, decimal digits, punctuation marks and so on. They are represented by codes that are usually six to eight bit long. Figure (b) indicate how 4 characters in either the ASCII or EBCDIC codes are stored in a 32 bit word.

To store an instruction, one part of the word specifies the operation to be performed. Other parts may be used to specify operand addresses. An example of a possible format for a 32 bit machine instruction. The 8 bit operation field can encode 28 (=256) distinct instructions, and the 24 bit address field can encode an address in the range (1) through 224 – 1 (=16777215).

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