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1. Theme 1: Number Crunching Machine The figure shows a number crunching machine in which any integer can be fed as input. There are a set of instructions which produces output as follows: If a positive integer is fed into the number crunching machine, it produces one of two results: If the integer fed in is EVEN, the machine divides the number by 2. If the integer fed in is ODD, the machine subtracts one from the number. If a negative integer is fed into the number crunching machine, it produces its additive inverse. Question1. Find the result when the following numbers are fed into the machine: (i) 123 (ii) -72 Question2. What can be the input to the machine if the output is 18? (a) 36 (b) 19 (c) -18 (d) All of the above Question3. It is possible to feed the output from the machine back into the input, and continue to do so until the output reaches zero. For example, with an initial input of 11, the following would occur: 11¬¬¬---- 10----- 5---- 4----- 2----- 1----- 0 We see that 6 steps are required to reach zero. Give the number of steps required to reach zero if you start with -24. Show the steps.​

1 Theme 1 Number Crunching Machine The figure shows a number crunching machine in which any integer can be fed as input There are a set of instructions which pr class=

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Answer:

Question 1:

(i) When 123 is fed into the machine:

  Since 123 is odd, the machine subtracts one from it.

  Result: 123 - 1 = 122

 

(ii) When -72 is fed into the machine:

  Since -72 is negative, the machine produces its additive inverse.

  Result: Additive inverse of -72 = 72

Question 2:

To find the possible input for the output 18, we need to backtrack the steps:

- If the output is even, it means the input must have been doubled.

- If the output is odd, it means the input was the result of adding one.

Since 18 is even, it suggests that the input was halved at some point.

So, the input must have been doubled to reach 18. Thus, the possible input is 36. Option (a) 36 is correct.

Question 3:

Starting with -24:

-24 -> 12 (Halving)

12 -> 6 (Halving)

6 -> 3 (Subtracting one)

3 -> 2 (Subtracting one)

2 -> 1 (Halving)

1 -> 0 (Subtracting one)

So, it takes 6 steps to reach zero from -24.

Step-by-step explanation:

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