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When calculations are carried out electronically they will usually be in binary or twos complement notation, but the result will very probably need to be displayed in decimal form. A binary number with its bits xecimal values of 1, 2, 4, 8, 16 etc. What is needed is a system where a group of binary digits can represent the decimal numbersand the next group etc.
To make this possible, binary codes are used that have ten values, but where each decima, is represented by the 1s and 0s of a binary code.
There are several different BCD codes, but they have a basic similarity. Each of the ten decimal digits 0 to 9 is represented by a group of 4 binary bits, but in codes the binary equivalents of the 10 decimal numbers do not necessarily need to be in a consecutive order.
Any group of 4 bits can represent any decimal value, so long as the relationship for that particular code is known. In fact any ten of the 16 available four bit combinations could be used to represent 10 decimal numbers, and this is where different BCD codes vary. There can be advantages in some specialist applications in using some particular decodificaeor of BCD. For example it may be useful to have a BCD code that can be used for calculations, decijal means having positive and negative values, similar to the twos complement system, but BCD codes are most often used for the display of decimal digits.
Decoificador this version the numbers 0 to 9 are represented by their pure binary equivalents, 4 bits per decimal number, in consecutive order. The least significant bit lsb has the weight or value 1, the next bit, going left, the value 2. The next bit has the value 4, and the most significant bit msb the value 8, as shown in Table 1.
So the BCD code for the decimal number 6 10 is Check this from Table 1. For numbers greater than 9 the system is extended by using a second block of 4 bits to represent tens and a third block to represent hundreds etc.
Therefore BCD acts as a half way stage between binary and true decimal representation, often preparing the result of a pure binary calculation for display on a decimal numerical display. Although BCD can be cecodificador in calculation, the values are not the same as pure decodoficador and must be treated differently if correct results decodificadro to be obtained. The facility to make calculations in BCD is included in some microprocessors.
One of the main drawbacks of BCD is that, because sixteen values are available from four bits, but only ten are used, there are several redundant values whichever BCD system is used. This defodificador wasteful in terms of circuitry, as the fourth bit the 8s column is under used. Depending on the type of display some further code conversion may also be needed.
One popular type of decimal display is the 7 segment display used in LED and LCD numerical displays, where any decimal digit is made up of 7 segments arranged as a figure 8, with an extra LED or LCD dot that can be used as a decimal point, as shown in Fig 1.
These displays therefore require 7 inputs, one to each of the LEDs a to g the decimal point is usually driven separately. Therefore the 4 bit output in BCD must be converted to bccd the correct 7 bit pattern of outputs to drive the display.
BCD to 7 segment decoders implement a logic truth table such as the one illustrated in Table 1. There are different types of display implemented by different types of decoder, notice in table 1.
Why would this be, and what effect would it have on the display? Notice that the 4 bit input to the decoder illustrated in Table 1. Although BCD is the most commonly used version of BCD, a number of other codes exist using other values of weighting.
Convert 8bit binary number to BCD in VHDL – Stack Overflow
Some of the more common variations are shown in Table 1. The weighting values in these codes are not randomly chosen, but each has particular merits for specific applications. Some codes are more useful for displaying decimal results with fractions, as with financial data. With others it is easier to assign positive and negative values to numbers. Some values in these BCD codes can also have alternative 1 and 0 combinations using the same weighting and are designed to improve calculation or error detection in specific systems.
Binary codes are not only used for data output.
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Another special binary code that is extensively used for reading positional information on mechanical devices edcimal as rotating shafts is Gray Code. The binary values are encoded onto a rotating disk Fig. As only one sensor sees a change at any one time, this reduces errors that may be created as the sensors pass from light to dark 0 to 1 or back again.
The problem with this kind of sensing is that if two or more sensors are allowed to change simultaneously, it cannot be guaranteed that the data from the sensors would change at exactly the same time.
If this happened there would be a brief deocdificador when a wrong binary code may be generated, suggesting that the disk is in a different position to its actual position. The one bit at a time feature of gray code effectively eliminates such errors. Notice also that the sequence of binary values also rotates continually, with the code for 15 changing back to 0 with only 1 bit changing.
With a 4 bit coded disk as illustrated in Fig. Hons All rights reserved. Learn about electronics Digital Electronics. After studying this section, you should be able to: Understand binary coded decimal.