To determine the number of addition and subtraction operations when multiplying two signed 2's complement numbers using Booth's algorithm, we need to follow these steps:

1. Booth's algorithm operates on the principle of examining bits of the multiplier (Q) paired with an additional "0" bit initially appended to the right.
2. For the given multiplier Q = 1010 0100 1010 1010, consider bit pairs (Q_i, Q_i-1), starting from the rightmost bit.
3. Evaluate each bit pair as follows:
   • If (Q_i, Q_i-1) = (0,1), perform M + AC (Accumulator).
   • If (Q_i, Q_i-1) = (1,0), perform M - AC.
   • If (Q_i, Q_i-1) = (0,0) or (1,1), no operation is performed.
4. Count the transitions as described in the bit pairs of Q extended with an appended zero at the right:

Count each unique transition:

• The extended bit sequence becomes: ... 0 1010 0100 1010 1010.
• Count transitions from '01' to '10' and '10' to '01' across 16 bits of Q, while considering only significant changes.
• Analyze: 1010 0100 1010 1010 corresponds to:
  1010 → 0100: 1 subtraction
  0100 → 1010: 1 addition
  1010 → 1010: 2 operations
  Total operations from this count = 13.

Booth's algorithm requires 13 addition or subtraction operations in total, confirming our result is within the specified range of 13,13.