The following two signed 2's complement numbers (multiplicand M and multiplier Q) are being multiplied using Booth's algorithm: M: 1100 1101 1110 1101 and Q: 1010 0100 1010 1010 The total number of addition and subtraction operations to be performed is __________. (Answer in integer)

In Booth's multiplication algorithm, the multiplier $Q$ is scanned from right to left (LSB to MSB) along with an appended bit $Q_{-1} = 0$.

The operations performed for each pair of adjacent bits $(Q_i, Q_{i-1})$ are:

• $01$: Addition ($+M$)

• $10$: Subtraction ($-M$)

• $00$ or $11$: No addition or subtraction (only shift)

Given the 16-bit multiplier $Q$ and $Q_{-1} = 0$:

Let us evaluate each bit pair $(q_i, q_{i-1})$ starting from $i = 0$ to $15$:

1. $(q_0, Q_{-1}) = (0, 0) \rightarrow$ No operation

2. $(q_1, q_0) = (1, 0) \rightarrow$ Subtraction

3. $(q_2, q_1) = (0, 1) \rightarrow$ Addition

4. $(q_3, q_2) = (1, 0) \rightarrow$ Subtraction

5. $(q_4, q_3) = (0, 1) \rightarrow$ Addition

6. $(q_5, q_4) = (1, 0) \rightarrow$ Subtraction

7. $(q_6, q_5) = (0, 1) \rightarrow$ Addition

8. $(q_7, q_6) = (1, 0) \rightarrow$ Subtraction

9. $(q_8, q_7) = (0, 1) \rightarrow$ Addition

10. $(q_9, q_8) = (0, 0) \rightarrow$ No operation

11. $(q_{10}, q_9) = (1, 0) \rightarrow$ Subtraction

12. $(q_{11}, q_{10}) = (0, 1) \rightarrow$ Addition

13. $(q_{12}, q_{11}) = (0, 0) \rightarrow$ No operation

14. $(q_{13}, q_{12}) = (1, 0) \rightarrow$ Subtraction

15. $(q_{14}, q_{13}) = (0, 1) \rightarrow$ Addition

16. $(q_{15}, q_{14}) = (1, 0) \rightarrow$ Subtraction

Counting all addition and subtraction operations:

• Number of subtractions ($10$ transitions) = $7$

• Number of additions ($01$ transitions) = $6$