BCD = Binary Coded Decimal

# BCD = Binary Coded Decimal

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## BCD = Binary Coded Decimal

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1. BCD = Binary Coded Decimal

2. Representing numbers • Integers • 2’s complement is most popular • BCD • Real numbers • Floating point • IEEE 754 standard format is most popular • Fixed point • 2’s complement integers (using standard integer arithmetic) • BCD • All of the above are supported by IA32!

3. BCD = binary coded decimal 4 bit encoding of 0..9 (decimal) base 10 base 2 BCD 0 0000 0000 same 1 0000 0001 " 2 0000 0010 " 3 0000 0011 " 4 0000 0100 " 5 0000 0101 " 6 0000 0110 " 7 0000 0111 " 8 0000 1000 " 9 0000 1001 " 10 0000 1010 0001 0000 11 0000 1011 0001 0001 12 0000 1100 0001 0010 . . . ? ? ?

4. BCD = binary coded decimal 4 bit encoding of 0..9 (decimal) base 10 base 2 BCD 0 0000 0000 same 1 0000 0001 " 2 0000 0010 " 3 0000 0011 " 4 0000 0100 " 5 0000 0101 " 6 0000 0110 " 7 0000 0111 " 8 0000 1000 " 9 0000 1001 " 10 0000 1010 0001 0000 11 0000 1011 0001 0001 12 0000 1100 0001 0010 … … … 99 0110 0011 1001 1001 100 0110 0100 invalid … … invalid 255 1111 1111 invalid

5. Why BCD? • What happened when we converted 0.10 (base 10) to base 2? 0.10 x 2 = 0.20 .0 0.20 x 2 = 0.40 0 0.40 x 2 = 0.80 0 0.80 x 2 = 0.60 1 0.60 x 2 = 0.20 1 . . .