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Booth Multipliers

This document explains the digital binary multiplication of two binary numbers, X and Y, using shift and add techniques. It details how to manage the binary representations, including the processes of shifting, adding, and subtracting in binary arithmetic. The final results include the multiplication of X (0010 or 2) by Y (0011 or 3), yielding 6, and subsequently the multiplication of X (1100 or -4) by Y (0010 or 2), yielding -8. The document emphasizes handling binary shifts and arithmetic logic throughout the operations.

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Booth Multipliers

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  1. Booth Multipliers

  2. U V X 0000 0000 0010 0 0000 0000 0010 00 Shift 0000 0000 0010 1101 0000 0010 1101 0000 0010 1110 1000 0010 10 Sub (add -y) + Shift 1110 1000 0010 0011 0000 0010 0001 1000 0010 0000 1100 0010 +Y 01 Add + shift 0000 1100 0010 0000 0110 00 shift Final Answer=6 Multiply X by Y X=0010 (2) Y=0011(3) -y=1101 Note: we shift both U|V ai ai-1 0 0 Shift 1 1 Shift 0 1 Add+Shift 1 0 Sub+shift -Y

  3. U V X 0000 0000 1100 0 0000 0000 1100 00 Shift 0000 0000 1100 0000 0000 1100 00 Shift 0000 0000 1100 1110 0000 1100 1110 0000 1100 1111 0000 1100 -Y 10 Sub (add –y) and shift 1111 0000 1100 1111 1000 11 Shift Result 1111 1000 = -8 Multiply X by Y X=1100(-4) Y=0010(2) -y=1110 Note: we shift both U|V ai ai-1 0 0 Shift 1 1 Shift 0 1 Add+Shift 1 0 Sub+shift

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