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.

• 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.

DecimalDigit

BCD8 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