Error Detection Codes

Binary information transmitted through some form of communication medium is subject to external noise that could change bits from 1 to 0, and vice versa. An error detection code is a binary code that detects digital errors during transmission. The detected errors cannot be corrected but their presence is indicated. The usual procedure is to observe the frequency of errors. If errors occur infrequently at random, the particular erroneous information is transmitted again. If the error occurs too often, the system is checked for malfunction.

parity bit: The most common error detection code used is the parity bit. A parity bit is an extra bit included with a binary message to make the total number of 1's either odd or even. A message of three bits and two possible parity bits is shown in Table 3-7. The P(odd) bit is chosen in such a way as to make the sum of 1's (in all four bits) odd. The P(even) bit is chosen to make the sum of all 1's even. In either case, the sum is taken over the message and the P bit. In any particular application, one or the other type of parity will be adopted. The even-parity scheme has the disadvantage of having a bit combination of all O's, while in the odd parity there is always one bit (of the four bits that constitute the message and P) that is 1. Note that the P(odd) is the complement of the P(even).

parity generator: Dunng rransfer of information from one location to another, the parity bit is handled as follows. At the sending end, the message (in this case three bits) is applied to a parity generator, where the required parity bit is generated. The message, including the parity bit, is transmitted to its destination. At the receiving end, all the incoming bits (in this case, four) are applied to a parity checker that checks the proper parity adopted (odd or even). An error is detected if the checked parity does not conform to the adopted parity. The parity method detects the presence of one, three, or any odd number of errors. An even number of errors is not detected.

Frequently Asked Questions

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Ans: The ASCII code (Table 3-4) is the standard code commonly used for the transmission of binary information. Each character is represented by a 7-bit code and usually an eighth bit is inserted for parity (see Sec. 3-6). The code consists of 128 characters. Ninety-five characters represent graphic symbols that include upper- and lowercase letters, numerals zero to nine, punctuation marks, and special symbols view more..
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Ans: Binary codes for decimal digits require a minimum of four bits. Numerous different codes can be formulated by arranging four or more bits in 10 distinct possible combinations. A few possibilities are shown in Table 3-6. view more..
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Ans: In previous sections we introduced the most common types of binary-coded data found in digital computers. Other binary codes for decimal numbers and alphanumeric characters are sometimes used. Digital computers also employ other binary codes for special applications. A few additional binary codes encountered in digital computers are presented in this section. view more..
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Ans: Binary information transmitted through some form of communication medium is subject to external noise that could change bits from 1 to 0, and vice versa. An error detection code is a binary code that detects digital errors during transmission. The detected errors cannot be corrected but their presence is indicated. The usual procedure is to observe the frequency of errors. If errors occur infrequently at random, the particular erroneous information is transmitted again. If the error occurs too often, the system is checked for malfunction view more..
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Ans: Parity generator and checker networl<s are logic circuits constructed with exclusive-OR functions. This is because, as mentioned in Sec. 1·2, the exclusive-OR function of three or more varia.bles is by definition an odd function. An odd function is a logic function whose value is binary 1 if, and only if, an odd function number of variables are equal to 1. According to this definition, the P( even) is the exclusive-OR of x, y, and l because it is equal to 1 when either one or all three of the variables are equal to I (Table 3-7). The P(odd) function is the complement of the P(even) function. view more..
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Ans: A digital system Is an interconnection of digital hardware module. that at'ClOinpl.lsh a specific Wormation-proceaslna taslc. Digital systems vary in size and complexi.ty interacting digital &om a few integrated circuits to a complex of interconnected and computers. Digital system design invariably UBeS a modular approach. The modules are constructed &om such digital components as ules registet&, are in decoders, terconnected arithmetic with common elements data and control paths , and control logic. The to fonn various moda digital computer system. view more..
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Ans: The symbolic notation used to describe the microoperation transfers among registers is called a register transfer language. The term "register transfer" implies the availability of hardware logic circuits that can perform a stated microoperation and transfer the result of the operation to the same or another register. view more..
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Ans: Computer registers are designated by capital letters (sometimes followed by numerals) to denote the function of the register. For example, the register that holds an address for the memory unit is usually called a memory address register and is designated by the name MAR. view more..
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Ans: where P is a control signal generated in the control section. It is sometimes convenient to separate the control variables from the register transfer operation by specifying a control function. view more..
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Ans: A typical digital computer has many registers, and paths must be provided to transfer information from one register to another. The number of wires will be excessive if separate lines are used between each register and all other registers in the system. view more..
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Ans: The two selection lines S1 and S0 are connected to the selection inputs of all four multiplexers. The selection lines choose the four bits of one register and transfer them into the four-line common bus. When S1S0 = 00, the 0 data inputs of all four multiplexers are selected and applied to the outputs that form the bus view more..
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Ans: A bus system can be constructed with three-state gates instead of multiplexers. A three-state gate is a digital circuit that exhibits three states. Two of the states are signals equivalent to logic 1 and 0 as in a conventional gate. The third state is a high-impedance state. view more..
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Ans: The operation of a memory unit was described in Sec. 2-7. The transfer of information from a memory word to the outside environment is called a read operation. view more..
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Ans: To implement the add microoperation with hardware, we need the registers that hold the data and the digital component that performs the arithmetic addition. The digital circuit that forms the arithmetic sum of two bits and a previous carry is called a full-adder . view more..
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Ans: The subtraction of binary numbers can be done most conveniently by means of complements as discussed in Sec. 3-2. Remember that the subtraction A - B can be done by taking the 2's complement of B and adding it to A. The 2's complement can be obtained by taking the 1' s complement and adding one to the least significant pair of bits. The 1's complement can be implemented with inverters and a one can be added to the sum through the input carry. view more..
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Ans: The increment microoperation adds one to a number in a register. For example, if a 4-bit register has a binary value 0110, it will go toO! II afterit is incremented. This microoperation is easily implemented with a binary counter view more..
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Ans: Logic microoperations specify binary operations for strings of bits stored in registers. These operations consider each bit of the register separately and treat them as binary variables. For example, the exclusive-OR microoperation with the contents of two registers . view more..
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Ans: There are 16 different logic operations that can be performed with two binary variables. They can be determined from all possible truth tables obtained with two binary variables as shown in Table 4-5. In this table, each of the 16 columns F0 through F15 represents a truth table of one possible Boolean function for the view more..
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