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)
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:
- 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.
- For the given multiplier Q = 1010 0100 1010 1010, consider bit pairs (Qi, Qi-1), starting from the rightmost bit.
- Evaluate each bit pair as follows:
- If (Qi, Qi-1) = (0,1), perform M + AC (Accumulator).
- If (Qi, Qi-1) = (1,0), perform M - AC.
- If (Qi, Qi-1) = (0,0) or (1,1), no operation is performed.
- Count the transitions as described in the bit pairs of Q extended with an appended zero at the right:
| Bit Pairs | Transition | Operation |
| 10 → 01 | 2 | M - AC, M + AC |
| 01 → 10 | 2 | M + AC, M - AC |
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.
Important Questions from Numerical Computation
Ratio of the angles of a triangle are 1 : 2 : 6. What is the smallest angle?
It would take one machine 4 hours to complete a production order and another machine 2 hour to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is ________ hours.
Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_remaining in the budget.
What is the value of \(1 + \frac{1}{4} + \frac{1}{{16}} + \frac{1}{{64}} + \frac{1}{{256}} + \ldots ?\)
A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?
