Number System and Codes

What is Gray code? (Definition, Conversions & Examples): This Gray code belongs to a class of codes called minimum-change code, in which only one bit in the code group changes when going from one step to the next. This is an unweighted code, which means that there are no specific weights assigned to the bit …

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What is Excess-3 Code? (Definition and Examples) The excess-3 code, abbreviated as XS-3, is an important 4-bit code sometimes used with binary-coded decimal (BCD) numbers. It possesses advantages in certain arithmetic operations. The excess-3 code for a decimal number can be obtained in the same manner as BCD except that 3 is added to each …

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What is Binary Coded Decimal (BCD) Code?: The 8-4-2-1 code or simply the Binary Coded Decimal code is composed of four bits representing the decimal digits 0 through 9, 8, 4, 2 and 1 are the weights of the four bits (23, 22, 21, 20) of each decimal digit similar to straight binary number system. …

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Hexadecimal Number System (Definition, Conversions & Examples): The binary number system forms the natural choice for the two-state systems. But in this system, the numbers tend to get short rather long. Hence to reduce the length of a given number it is quite common to use hexadecimal system. The hexadecimal number system has a base …

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Octal Number System (Definition, Conversions & Examples): The number system with base (or radix) eight is known as the octal number system. Although we can use any eight digits, it is customary to use the first eight decimal digits: 0, 1, 2, 3, 4, 5, 6, 7. There is no 8 or 9 in octal …

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What is a Floating Point Number? The real numbers considered so far were represented in what is known as fixed point notation. In such notation, the position of the decimal is fixed for a fixed number of bits. For example, a number say 725.632 can be stored in a 6 bit register as shown in …

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What is Double Precision System? For any computer, the word length is fixed. Most present day computers are 16 bit and in a 16 bit computer, that is, in a computer with 16-bit word length, only numbers from +216-1 – 1 (i.e., +32.767) to -216-1 (i.e., -32,768) can be stored in each register. To store numbers …

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Signed Binary Numbers (Definition, Conversions & Examples): In the decimal number system, a plus (+) sign is used for denoting a positive number and a minus (-) sign for denoting a negative number. The plus sign is normally dropped, and absence of any sign means the number is positive one. This representation of numbers is …

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Binary Number System (Definition, Conversions & Examples): The binary number system is simply another way to count. It is less complicated than the decimal number system because it is composed of only two digits 0 and 1. Just as the decimal system with its ten digits is a base-10 system, the binary system with its …

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