Number system,base and symbols




Table 2.1 Number systems, bases, and symbols Number system Base Digital symbols Binary 2 0, 1 Ternary 3 0, 1, 2 Quaternary 4 0, 1, 2, 3 Quinary 5 0, 1, 2, 3, 4 Octal 8 0, 1, 2, 3, 4, 5, 6, 7 Decimal 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Duodecimal 12 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B Hexadecimal 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F Vigesimal 20 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J



Frequently Asked Questions

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Ans: Most people today use decimal representation to count. This number system uses TEN different symbols to represent values. In the decimal system there are 10 digit symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 with 0 having the least value and 9 having the greatest value. For a number represented in decimal system, the digit on the extreme left has the greatest value, whereas the digit on the extreme right has the least value. view more..
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Ans: The base, or radix, of any number system is determined by the number of digit symbols in the system. For example, binary is a base-2 number system since it uses two symbols and decimal is a base-10 system since it uses ten symbols. view more..
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Ans: A number system defines a set of values used to represent quantity. For example, the number of mobile phones kept in a shop, the number of persons standing in a queue, and the number of students attending a class. view more..
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Ans: Table 2.1 Number systems, bases, and symbols Number system Base Digital symbols Binary 2 0, 1 Ternary 3 0, 1, 2 Quaternary 4 0, 1, 2, 3 Quinary 5 0, 1, 2, 3, 4 Octal 8 0, 1, 2, 3, 4, 5, 6, 7 Decimal 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Duodecimal 12 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B Hexadecimal 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F Vigesimal 20 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J view more..
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Ans: To convert a hexadecimal to decimal, begin by multiplying each of the hexadecimal digits by their positional weight values as expressed in decimal. Then the resulting values are added to obtain the value of the decimal number. view more..
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Ans: To convert from decimal whole numbers to octal, the systematic approach called the repeated-division-by-8 method is used. This method is explained by the following Converting (359)10 to octal. (a) Divide the decimal number by eight and obtain a quotient and a remainder. (b) Divide the quotient by eight and obtain a new quotient and a remainder. (c) Repeat step (b) until the quotient is equal to zero (0). (d) The first remainder produced is the LSB in the octal number and the last remainder (R) is the MSB. Accordingly, the octal number is then written (from left to right) with the MSB occurring first. view more..
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Ans: To express the value of a given octal number as its decimal equivalent, add the octal digits after each digit has been multiplied by its associated weight. view more..
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Ans: A binary number is made of 0s and 1s. In the binary number system only two symbols, 0 and 1, are used to represent numeric values. The symbol “0“ represents the value “zero” while the symbol “1” represents the value “one”. Since there are only two symbols in the binary number system, the value “two” is represented by placing the symbol “1” on the left–hand side of the symbol “0” resulting in the binary equivalent “10”. Next, the value “three” is represented by “11” in the binary number systemby replacing the “ 0 ” in “10” by the next higher value symbol “1”. view more..
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Ans: The abbreviated form of “ bi-nary dig-it ” is known as bit. When a “bit” is mentioned, it means a single binary digit, which may either be a “0” or “1”, is referred to. view more..
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Ans: All modern computers use semiconductor memory as primary memory. One of the important semiconductor memories used in desktop computers is Random Access Memory (RAM). Here “random access” means that any storage location can be accessed (both read and write) directly. view more..
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Ans: It is another type of memory that retains data and instructions stored in it even when the power is turned off. ROM is used in personal computers for storing start-up instructions provided by the manufacturer for carrying out basic operations such as bootstrapping in a PC, and is programmed for specific purposes during their fabrication. view more..
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Ans: There are four main types of secondary storage devices available in a computer system: Disk drives CD drives (CD-R, CD-RW, and DVD) Tape drives USB flash drives view more..
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Ans: Cache memory It is a special high-speed memory that allows a microprocessor to access data more rapidly than from memory located elsewhere on the system board. view more..
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Ans: A microprocessor is an integrated circuit chip that contains all of the essential components for the central processing unit (CPU) of a microcomputer system. view more..
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Ans: 1’s complement A number system that was used in some computers to represent negative numbers. To form 1s complement of a number, each bit of the number is inverted which means zeros are replaced with ones and ones with zero. view more..
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Ans: 1’s complement A number system that was used in some computers to represent negative numbers. To form 1s complement of a number, each bit of the number is inverted which means zeros are replaced with ones and ones with zero. view more..
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Ans: 2’s complement A number formed by adding 1 to the 1’s compliment of a number. The 2’s complement representation has become the standard method of storing signed binary integers. It allows the representation of an n-bit number in the range – 2n to 2n-1, and has the significant advantage of only having one encoding for 0. view more..
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Ans: A Boolean or logic expression is a logic variable or a number of logic variables involved with one another through the logical operations ‘.’, ‘+’, and ‘–’. view more..




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