Bcd To Xs3 Code Converter For Samsung
Bcd to excess 3 code converter • 1. BCD to EXCESS 3 Code Converter By Ushaswini chowdary.M • Introduction • The availability of large variety of codes for the same discrete elements of information results in the use of different codes by the different systems.
The design process we use to synthesize the BCD to Excess-3 code converter is simple, and you should use it to design your combinational circuits.
• A conversion circuit must be inserted between the two systems if each use different codes for the same information. • Thus a code converter is a circuit that makes the two systems compatible even though both uses different binary information. • • Code converters, more specifically encoders and decoders, have been used to protect private information. • Indeed, code converters have proven to be so effective that the National Security Agency (NSA) has made a career out of creating and breaking codes. • To convert from binary to excess 3 code the input lines must supply the bit combination of elements as specified by the code. • Binary Coded Decimal • The term BCD refers to representing the ten decimal digits in binary forms; which simply means to count in binary. • In computing and electronic systems, binary coded decimal is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight, although other sizes (such as six bits) have been used historically.
Special bit patterns are sometimes used for a sign or for other indications (e.g., error or overflow). • • BCD takes advantage of the fact that any one decimal numeral can be represented by a four bit pattern. This is also called '8421' encoding. Decimal Digit BCD 8 4 2 1 0 0 0 0 0 1 0 0 0 1 2 0 0 1 0 3 0 0 1 1 4 0 1 0 0 5 0 1 0 1 6 0 1 1 0 7 0 1 1 1 8 1 0 0 0 9 1 0 0 1 • Excess 3 • It is a non weighted code. • In XS-3, numbers are represented as decimal digits, and each digit is represented by four bits as the digit value plus 3 (the 'excess' amount).
• The primary advantage of XS-3 coding over non-biased coding is that a decimal number can be nines' complemented as easily as a binary number can be ones' complemented. In addition, when the sum of two XS-3 digits is greater than 9, the carry bit of a four bit adder will be set high. • • The Excess-3 BCD system is formed by adding 0011 to each BCD value as in Table 2. For example, the decimal number 7, which is coded as 0111 in BCD, is coded as 0111+0011=1010 in Excess-3 BCD.
Decimal Numerals Excess-3 0 0011 1 0100 2 0101 3 0110 4 0111 5 1000 6 1001 7 1010 8 1011 9 1100 • THE BCD TO EXCESS 3 CODE CONVERTER • BCD Excess-3 circuit will convert numbers from their binary representation to their excess-3 representation. Hence our truth table is as below: B3 B2 B1 B0 E3 E2 E1 E0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 • K maps • Our task now is to use the truth table to find four switching expressions: one for E3, one for E2, one for E1, and one for E0. We have two choices: we can use Boolean algebraic manipulations, or we can use Karnaugh maps. • We use k maps for simplicity. Here don’t cares are available because in the truth table in Table 3, no BCD valuations exist for E3E2E1E0 = 1010,1011,1100,1101,1110,1111. As such, we evaluate B3B2B1B0= xxxx (either 0 or 1).
• E3=B3+B2(B1+B0) • E2=B2^(B1+B0) • E1=(B1^B0)’ • E0=B0’ • Block diagram • Applications • Excess-3 was used on some older computers • Cash registers • Hand held portable electronic calculators.
To convert a decimal number into BCD, you take 4 bit binary of all the digits of the decimal number. For example, to convert 54D (D stands for Decimal) into BCD, you considere 4 bit binary of 5 and 4 respectively. Which gives 0101 0100. For XS3 (Remember Excess 3), all you need to do it add 3 to each digits of the decimal number and then consider 4 bit binaries of the resulting digits. The same number, 54 D to be converted into XS3, add 3 to each digits, which give us 8 and 7. Roger Eno Voices Rar Files here.
And the resultant 4 digit binaries are 1000 and 0111. Thus XS 3 for 54D is 1000 0111. Now, to convert a BCD directly into XS 3, all you need to do is add 11B (B stands for binary) to each 4 bits of the BCD.
If you add 11 to 0101 and 0100, you get 0100 and and 0111. These two taken together is the XS 3 of the given BCD.
A good explanation for the purpose of XS-3, also known as Stibitz code, can be found on Wikipedia. The purpose for this “biased” code is to allow subtraction by means of compliment addition. Each decimal digit, in turn, is expressed as four binary digits after having added 3. You do not add 3 to 67, you add 3 in turn to 6 and 7 and express as groups of four binary digits: 67 is expressed in XS-3 as 1001 1010.
The basic purpose for the conversion, again, is to allow subtraction by means of the addition of the subtrahends compliment.
Why this conversion is done can be also regarded as what is the importance of the excess 3 code or what will be it’s applications Application of Excess-3 Because of many shortcomings in addition of the BCD code, excess 3 code is used and grey code is used in the shaft position of the airplanes. These codes are precisely used in electro optical switches and electrochemical signals. The Gray code arises in many real life situations. In the beginning, the main use of the code was related to what we now call as the conversion from analog to digital format.
The basic aim was to convert a voltage value which was previously in analog to the corresponding series of pulse which will represent the same value in digital form. This technique was to convert voltage by displacing vertically an electron beam that sweeps horizontally across the screen of the cathode ray tube. The screen having a masked imprint on it only allows a passage of beam in certain places, and a current was generated till the beam was passing through the mask. The passage of the beam gives rise to a series of ‘on’ and ‘off’ conditions corresponding to the pattern of the holes through which it passes. The most common use of Gray code is locating for rotational position of the shafts I which a pattern which represents the grey code is printed on a disk, or on the shaft, and the pattern is sensed by an electrical or optical detector. Gray Code was used in some old computers that relied on a pre-specified number N as a biasing value.
The excess 3 code is a technique to represent numbers with a balance of positive and negative numbers. When the sum of two of these excess 3 numbers exceed 9, the carry bit of adder will set to high. When you add two excess 3 numbers, the resultant would not be an excess 3 number, example: add 1 to 3, the answer would seem to be 7 but the actual answer should be 4, so a remedy of this problem is to subtract 3 (binary 011) if the resultant is less than decimal 10 and add 3 if the number is equal to or greater than 10. This needs to be done due to the fact that whenever we add two numbers, an excess value of six results in the sum.
But we now that the values 0 to 15 are four bit integer and any excess to that means the sum will overflow. Hope this helps. Why the code is converted depends upon it’s applications Thanks for asking.