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Information about Primitive multiplication table based bcd multiplication

Primitive table based multiplication algorithm

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Challenge 1) Circuit Design to access ‘primitive multiplication result’ from PMT efficiently. Circuit design: Let input = I, smaller digit=sd Then larger digit=ld and sd*ld= T*10+U T= I( ld, sd) i.e. T is function of ld and sd Similarly, U= I(ld, sd) Use above function to build truth table and design circuit accordingly. Advantages 1) Many times, we are only interested in decimal result of computation. In such case, BCD multiplication is useful. Unlike binary multiplication, it avoids redundant conversion of ‘decimal operand to binary number’ and ‘binary result to decimal result’. Decimal operand result Decimal to Binary conversion Binary to Decimal conversion Binary multiplier Binary Decimal Result Binary Multiplication (Decimal-binary inter conversion overhead) 2) Lower complexity 3) Multiplication, division etc operations are ‘base specific’. Many multiplications like 999*967, 99986*100012 etc. are easy in decimal number system but hard and time consuming to compute in binary number system. 4) Vedic mathematics can be easily applied to decimal/BCD operand to reduce complexity of multiplication, division and other operation. Disadvantages: 1) Storing operand in BCD i.e. BCD operand requires more memory than binary operand 2) Additional memory or dedicated register set are required to store ‘primitive multiplication’. 3) More complex design.

Now let’s rearrange the multiplication table based on the primitive root 3. ... 15, we get the following multiplication table for those linear residues that are

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