Bcd to excess 3 code converter

BCD to excess 3 code converter

1. BCD to EXCESS 3 Code Converter By Ushaswini chowdary.M

2. 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. 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.

3. 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.

4. 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).

5. 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 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

6. 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.

7. 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 0011 1 0100 2 0101 3 0110 4 0111 5 1000 6 1001 7 1010 8 1011 9 1100

8. 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

9. K maps Our task now is to use the truth table to find four switching expressions: one for E 3 , one for E 2 , one for E 1 , and one for E . 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).

10. E3=B3+B2(B1+B0)

11. E2=B2^(B1+B0)

12. E1=(B1^B0)’

13. E0=B0’

14. Block diagram

15. Applications Excess-3 was used on some older computers Cash registers Hand held portable electronic calculators