Excess-3 (XS3) Code Converter
Convert decimal numbers to Excess-3 (XS3) code by adding 3 and encoding to BCD
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Excess-3 Principle
Excess-3 digit = decimal digit + 3
0+3=3=0011, 1+3=4=0100, 2+3=5=0101
5+3=8=1000, 9+3=12=1100
Each digit: add 3, then 4-bit BCD
Excess-3 (XS3) is a self-complementing BCD variant: subtract 3 to decode, add 3 to encode. Perfect for 9s complement subtraction in old computing.
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Only decimal digits 0-9 allowed. Each digit gets +3 before 4-bit BCD.
What Is Excess-3 Code?
Excess-3 (XS3) is a BCD variant where each digit is +3, then encoded as 4-bit BCD. Self-complementing simplifies 9s complement.
Self-Complementing
9s complement is bit-wise NOT, very useful for subtraction.
Easy Subtraction
Simplified 9s complement arithmetic in early computers.
Error Detection
Better error detection than standard BCD.
Legacy Systems
Used in older computers and calculators.
💡 Teaching Example: Convert 5 to XS3. Step 1: 5+3=8. Step 2: 8=1000. Step 3: Result is 1000.
Applications
Legacy Computing
Subtraction
Calculators
Error Detection
Frequently Asked Questions
How do you convert decimal to excess-3?▼
For each decimal digit, add 3 to get d+3, then convert d+3 to 4-bit BCD. Concatenate all nibbles.
What is excess-3 code used for?▼
Excess-3 is a self-complementing BCD variant used in old computers for subtraction and error detection.
What is the excess-3 code for 5?▼
5+3=8, 8 in 4-bit BCD is 1000. So excess-3 for 5 is 1000.
Is excess-3 self-complementing?▼
Yes, 9s complement is just bit-wise NOT of excess-3 code, making it self-complementing.
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