In fact it can be shown that any decimal number in

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Unformatted text preview: of 0s and Is are possible and from Figure 3.1 it may be seen that a 3-bit number can have one of the 8 values in the range 0 to 7. In fact, it can be shown that any decimal number in the range 0 to 2""1 can be represented in the binary form as an n-bit number. I Biliary Decimal Equivalent 000 001 010 011 100 101 110 111 0 1 2 3 4 5 6 7 Figure 3.1. 3-bit numbers with their decimal values. Every computer stores numbers, letters, and other special characters in binary form. There are several occasions when computer professionals have to know the raw data contained in a computer's memory. A common way of looking at the contents of a computer's memory is to print out the memory contents on a line printer. This printout is called a memory dump. If memory dumps were to be printed using binary numbers, the computer professionals would be confronted with many pages of 0s and Is. Working with these numbers would be very difficult and error prone. Because of the quantity of printout that would be required in a memory dump of binary digits and the lack of digit variety (0s and Is only), two number systems, octal and hexadecimal, are used as shortcut notations for binary. These number systems and their relationship with the binary number system are explained below. Octal Number System In the octal number system the base is 8. So in this system there are only eight symbols or digits: 0, 1,2, 3, 4, 5, 6, and 7 (8 and 9 do not exist in this system). Here also the largest single digit is 7 (one less than the base). Again, each position in an octal number represents a power of the base (8). Thus the decimal equivalent of the octal number 2057 (written as 20578) is: (2 x 83) + (0 x 82) + (5 x 81) + (7 x 8°), or 1024 + 0 + 40 + 7, or 1071 Hence, 20578= 107110 Observe that since there are only 8 digits in the octal number system, 3 bits (2 3 = 8) are sufficient to represent any octal number in binary (see Figure 3.1). Hexadecimal Number System The hexadecimal number system is one with a base of 16. The base of 16 suggests choic...
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