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Fibonacci state traces

Set 2 of 3 · 32 worked questions. Predict your result before expanding the solution.

These worked traces are meant to build fluency through controlled variation. If several answers feel identical, try the next difficult value and look for the point where a carry, sign, branch, or selected memory address changes the outcome.

Sequential programs · Problem 0033

At Fibonacci iteration 32, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 32 begins with the pair of registers a=2178309, b=3524578.
  2. The current output is register a, so the emitted term is 2178309.
  3. Calculate a temporary sum t = a+b = 2178309+3524578 = 5702887.
  4. Copy the previous value of b into the new a register.
  5. The new a is 3524578.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 5702887.
  8. After the update, the pair is (3524578, 5702887).
  9. On the next iteration, the machine will emit 3524578.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 2178309; pair (3524578, 5702887)

Sequential programs · Problem 0034

At Fibonacci iteration 33, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 33 begins with the pair of registers a=3524578, b=5702887.
  2. The current output is register a, so the emitted term is 3524578.
  3. Calculate a temporary sum t = a+b = 3524578+5702887 = 9227465.
  4. Copy the previous value of b into the new a register.
  5. The new a is 5702887.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 9227465.
  8. After the update, the pair is (5702887, 9227465).
  9. On the next iteration, the machine will emit 5702887.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 3524578; pair (5702887, 9227465)

Sequential programs · Problem 0035

At Fibonacci iteration 34, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 34 begins with the pair of registers a=5702887, b=9227465.
  2. The current output is register a, so the emitted term is 5702887.
  3. Calculate a temporary sum t = a+b = 5702887+9227465 = 14930352.
  4. Copy the previous value of b into the new a register.
  5. The new a is 9227465.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 14930352.
  8. After the update, the pair is (9227465, 14930352).
  9. On the next iteration, the machine will emit 9227465.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 5702887; pair (9227465, 14930352)

Sequential programs · Problem 0036

At Fibonacci iteration 35, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 35 begins with the pair of registers a=9227465, b=14930352.
  2. The current output is register a, so the emitted term is 9227465.
  3. Calculate a temporary sum t = a+b = 9227465+14930352 = 24157817.
  4. Copy the previous value of b into the new a register.
  5. The new a is 14930352.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 24157817.
  8. After the update, the pair is (14930352, 24157817).
  9. On the next iteration, the machine will emit 14930352.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 9227465; pair (14930352, 24157817)

Sequential programs · Problem 0037

At Fibonacci iteration 36, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 36 begins with the pair of registers a=14930352, b=24157817.
  2. The current output is register a, so the emitted term is 14930352.
  3. Calculate a temporary sum t = a+b = 14930352+24157817 = 39088169.
  4. Copy the previous value of b into the new a register.
  5. The new a is 24157817.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 39088169.
  8. After the update, the pair is (24157817, 39088169).
  9. On the next iteration, the machine will emit 24157817.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 14930352; pair (24157817, 39088169)

Sequential programs · Problem 0038

At Fibonacci iteration 37, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 37 begins with the pair of registers a=24157817, b=39088169.
  2. The current output is register a, so the emitted term is 24157817.
  3. Calculate a temporary sum t = a+b = 24157817+39088169 = 63245986.
  4. Copy the previous value of b into the new a register.
  5. The new a is 39088169.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 63245986.
  8. After the update, the pair is (39088169, 63245986).
  9. On the next iteration, the machine will emit 39088169.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 24157817; pair (39088169, 63245986)

Sequential programs · Problem 0039

At Fibonacci iteration 38, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 38 begins with the pair of registers a=39088169, b=63245986.
  2. The current output is register a, so the emitted term is 39088169.
  3. Calculate a temporary sum t = a+b = 39088169+63245986 = 102334155.
  4. Copy the previous value of b into the new a register.
  5. The new a is 63245986.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 102334155.
  8. After the update, the pair is (63245986, 102334155).
  9. On the next iteration, the machine will emit 63245986.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 39088169; pair (63245986, 102334155)

Sequential programs · Problem 0040

At Fibonacci iteration 39, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 39 begins with the pair of registers a=63245986, b=102334155.
  2. The current output is register a, so the emitted term is 63245986.
  3. Calculate a temporary sum t = a+b = 63245986+102334155 = 165580141.
  4. Copy the previous value of b into the new a register.
  5. The new a is 102334155.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 165580141.
  8. After the update, the pair is (102334155, 165580141).
  9. On the next iteration, the machine will emit 102334155.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 63245986; pair (102334155, 165580141)

Sequential programs · Problem 0041

At Fibonacci iteration 40, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 40 begins with the pair of registers a=102334155, b=165580141.
  2. The current output is register a, so the emitted term is 102334155.
  3. Calculate a temporary sum t = a+b = 102334155+165580141 = 267914296.
  4. Copy the previous value of b into the new a register.
  5. The new a is 165580141.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 267914296.
  8. After the update, the pair is (165580141, 267914296).
  9. On the next iteration, the machine will emit 165580141.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 102334155; pair (165580141, 267914296)

Sequential programs · Problem 0042

At Fibonacci iteration 41, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 41 begins with the pair of registers a=165580141, b=267914296.
  2. The current output is register a, so the emitted term is 165580141.
  3. Calculate a temporary sum t = a+b = 165580141+267914296 = 433494437.
  4. Copy the previous value of b into the new a register.
  5. The new a is 267914296.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 433494437.
  8. After the update, the pair is (267914296, 433494437).
  9. On the next iteration, the machine will emit 267914296.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 165580141; pair (267914296, 433494437)

Sequential programs · Problem 0043

At Fibonacci iteration 42, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 42 begins with the pair of registers a=267914296, b=433494437.
  2. The current output is register a, so the emitted term is 267914296.
  3. Calculate a temporary sum t = a+b = 267914296+433494437 = 701408733.
  4. Copy the previous value of b into the new a register.
  5. The new a is 433494437.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 701408733.
  8. After the update, the pair is (433494437, 701408733).
  9. On the next iteration, the machine will emit 433494437.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 267914296; pair (433494437, 701408733)

Sequential programs · Problem 0044

At Fibonacci iteration 43, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 43 begins with the pair of registers a=433494437, b=701408733.
  2. The current output is register a, so the emitted term is 433494437.
  3. Calculate a temporary sum t = a+b = 433494437+701408733 = 1134903170.
  4. Copy the previous value of b into the new a register.
  5. The new a is 701408733.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 1134903170.
  8. After the update, the pair is (701408733, 1134903170).
  9. On the next iteration, the machine will emit 701408733.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 433494437; pair (701408733, 1134903170)

Sequential programs · Problem 0045

At Fibonacci iteration 44, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 44 begins with the pair of registers a=701408733, b=1134903170.
  2. The current output is register a, so the emitted term is 701408733.
  3. Calculate a temporary sum t = a+b = 701408733+1134903170 = 1836311903.
  4. Copy the previous value of b into the new a register.
  5. The new a is 1134903170.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 1836311903.
  8. After the update, the pair is (1134903170, 1836311903).
  9. On the next iteration, the machine will emit 1134903170.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 701408733; pair (1134903170, 1836311903)

Sequential programs · Problem 0046

At Fibonacci iteration 45, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 45 begins with the pair of registers a=1134903170, b=1836311903.
  2. The current output is register a, so the emitted term is 1134903170.
  3. Calculate a temporary sum t = a+b = 1134903170+1836311903 = 2971215073.
  4. Copy the previous value of b into the new a register.
  5. The new a is 1836311903.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 2971215073.
  8. After the update, the pair is (1836311903, 2971215073).
  9. On the next iteration, the machine will emit 1836311903.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 1134903170; pair (1836311903, 2971215073)

Sequential programs · Problem 0047

At Fibonacci iteration 46, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 46 begins with the pair of registers a=1836311903, b=2971215073.
  2. The current output is register a, so the emitted term is 1836311903.
  3. Calculate a temporary sum t = a+b = 1836311903+2971215073 = 4807526976.
  4. Copy the previous value of b into the new a register.
  5. The new a is 2971215073.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 4807526976.
  8. After the update, the pair is (2971215073, 4807526976).
  9. On the next iteration, the machine will emit 2971215073.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 1836311903; pair (2971215073, 4807526976)

Sequential programs · Problem 0048

At Fibonacci iteration 47, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 47 begins with the pair of registers a=2971215073, b=4807526976.
  2. The current output is register a, so the emitted term is 2971215073.
  3. Calculate a temporary sum t = a+b = 2971215073+4807526976 = 7778742049.
  4. Copy the previous value of b into the new a register.
  5. The new a is 4807526976.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 7778742049.
  8. After the update, the pair is (4807526976, 7778742049).
  9. On the next iteration, the machine will emit 4807526976.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 2971215073; pair (4807526976, 7778742049)

Sequential programs · Problem 0049

At Fibonacci iteration 48, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 48 begins with the pair of registers a=4807526976, b=7778742049.
  2. The current output is register a, so the emitted term is 4807526976.
  3. Calculate a temporary sum t = a+b = 4807526976+7778742049 = 12586269025.
  4. Copy the previous value of b into the new a register.
  5. The new a is 7778742049.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 12586269025.
  8. After the update, the pair is (7778742049, 12586269025).
  9. On the next iteration, the machine will emit 7778742049.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 4807526976; pair (7778742049, 12586269025)

Sequential programs · Problem 0050

At Fibonacci iteration 49, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 49 begins with the pair of registers a=7778742049, b=12586269025.
  2. The current output is register a, so the emitted term is 7778742049.
  3. Calculate a temporary sum t = a+b = 7778742049+12586269025 = 20365011074.
  4. Copy the previous value of b into the new a register.
  5. The new a is 12586269025.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 20365011074.
  8. After the update, the pair is (12586269025, 20365011074).
  9. On the next iteration, the machine will emit 12586269025.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 7778742049; pair (12586269025, 20365011074)

Sequential programs · Problem 0051

At Fibonacci iteration 50, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 50 begins with the pair of registers a=12586269025, b=20365011074.
  2. The current output is register a, so the emitted term is 12586269025.
  3. Calculate a temporary sum t = a+b = 12586269025+20365011074 = 32951280099.
  4. Copy the previous value of b into the new a register.
  5. The new a is 20365011074.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 32951280099.
  8. After the update, the pair is (20365011074, 32951280099).
  9. On the next iteration, the machine will emit 20365011074.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 12586269025; pair (20365011074, 32951280099)

Sequential programs · Problem 0052

At Fibonacci iteration 51, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 51 begins with the pair of registers a=20365011074, b=32951280099.
  2. The current output is register a, so the emitted term is 20365011074.
  3. Calculate a temporary sum t = a+b = 20365011074+32951280099 = 53316291173.
  4. Copy the previous value of b into the new a register.
  5. The new a is 32951280099.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 53316291173.
  8. After the update, the pair is (32951280099, 53316291173).
  9. On the next iteration, the machine will emit 32951280099.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 20365011074; pair (32951280099, 53316291173)

Sequential programs · Problem 0053

At Fibonacci iteration 52, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 52 begins with the pair of registers a=32951280099, b=53316291173.
  2. The current output is register a, so the emitted term is 32951280099.
  3. Calculate a temporary sum t = a+b = 32951280099+53316291173 = 86267571272.
  4. Copy the previous value of b into the new a register.
  5. The new a is 53316291173.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 86267571272.
  8. After the update, the pair is (53316291173, 86267571272).
  9. On the next iteration, the machine will emit 53316291173.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 32951280099; pair (53316291173, 86267571272)

Sequential programs · Problem 0054

At Fibonacci iteration 53, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 53 begins with the pair of registers a=53316291173, b=86267571272.
  2. The current output is register a, so the emitted term is 53316291173.
  3. Calculate a temporary sum t = a+b = 53316291173+86267571272 = 139583862445.
  4. Copy the previous value of b into the new a register.
  5. The new a is 86267571272.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 139583862445.
  8. After the update, the pair is (86267571272, 139583862445).
  9. On the next iteration, the machine will emit 86267571272.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 53316291173; pair (86267571272, 139583862445)

Sequential programs · Problem 0055

At Fibonacci iteration 54, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 54 begins with the pair of registers a=86267571272, b=139583862445.
  2. The current output is register a, so the emitted term is 86267571272.
  3. Calculate a temporary sum t = a+b = 86267571272+139583862445 = 225851433717.
  4. Copy the previous value of b into the new a register.
  5. The new a is 139583862445.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 225851433717.
  8. After the update, the pair is (139583862445, 225851433717).
  9. On the next iteration, the machine will emit 139583862445.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 86267571272; pair (139583862445, 225851433717)

Sequential programs · Problem 0056

At Fibonacci iteration 55, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 55 begins with the pair of registers a=139583862445, b=225851433717.
  2. The current output is register a, so the emitted term is 139583862445.
  3. Calculate a temporary sum t = a+b = 139583862445+225851433717 = 365435296162.
  4. Copy the previous value of b into the new a register.
  5. The new a is 225851433717.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 365435296162.
  8. After the update, the pair is (225851433717, 365435296162).
  9. On the next iteration, the machine will emit 225851433717.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 139583862445; pair (225851433717, 365435296162)

Sequential programs · Problem 0057

At Fibonacci iteration 56, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 56 begins with the pair of registers a=225851433717, b=365435296162.
  2. The current output is register a, so the emitted term is 225851433717.
  3. Calculate a temporary sum t = a+b = 225851433717+365435296162 = 591286729879.
  4. Copy the previous value of b into the new a register.
  5. The new a is 365435296162.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 591286729879.
  8. After the update, the pair is (365435296162, 591286729879).
  9. On the next iteration, the machine will emit 365435296162.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 225851433717; pair (365435296162, 591286729879)

Sequential programs · Problem 0058

At Fibonacci iteration 57, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 57 begins with the pair of registers a=365435296162, b=591286729879.
  2. The current output is register a, so the emitted term is 365435296162.
  3. Calculate a temporary sum t = a+b = 365435296162+591286729879 = 956722026041.
  4. Copy the previous value of b into the new a register.
  5. The new a is 591286729879.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 956722026041.
  8. After the update, the pair is (591286729879, 956722026041).
  9. On the next iteration, the machine will emit 591286729879.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 365435296162; pair (591286729879, 956722026041)

Sequential programs · Problem 0059

At Fibonacci iteration 58, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 58 begins with the pair of registers a=591286729879, b=956722026041.
  2. The current output is register a, so the emitted term is 591286729879.
  3. Calculate a temporary sum t = a+b = 591286729879+956722026041 = 1548008755920.
  4. Copy the previous value of b into the new a register.
  5. The new a is 956722026041.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 1548008755920.
  8. After the update, the pair is (956722026041, 1548008755920).
  9. On the next iteration, the machine will emit 956722026041.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 591286729879; pair (956722026041, 1548008755920)

Sequential programs · Problem 0060

At Fibonacci iteration 59, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 59 begins with the pair of registers a=956722026041, b=1548008755920.
  2. The current output is register a, so the emitted term is 956722026041.
  3. Calculate a temporary sum t = a+b = 956722026041+1548008755920 = 2504730781961.
  4. Copy the previous value of b into the new a register.
  5. The new a is 1548008755920.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 2504730781961.
  8. After the update, the pair is (1548008755920, 2504730781961).
  9. On the next iteration, the machine will emit 1548008755920.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 956722026041; pair (1548008755920, 2504730781961)

Sequential programs · Problem 0061

At Fibonacci iteration 60, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 60 begins with the pair of registers a=1548008755920, b=2504730781961.
  2. The current output is register a, so the emitted term is 1548008755920.
  3. Calculate a temporary sum t = a+b = 1548008755920+2504730781961 = 4052739537881.
  4. Copy the previous value of b into the new a register.
  5. The new a is 2504730781961.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 4052739537881.
  8. After the update, the pair is (2504730781961, 4052739537881).
  9. On the next iteration, the machine will emit 2504730781961.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 1548008755920; pair (2504730781961, 4052739537881)

Sequential programs · Problem 0062

At Fibonacci iteration 61, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 61 begins with the pair of registers a=2504730781961, b=4052739537881.
  2. The current output is register a, so the emitted term is 2504730781961.
  3. Calculate a temporary sum t = a+b = 2504730781961+4052739537881 = 6557470319842.
  4. Copy the previous value of b into the new a register.
  5. The new a is 4052739537881.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 6557470319842.
  8. After the update, the pair is (4052739537881, 6557470319842).
  9. On the next iteration, the machine will emit 4052739537881.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 2504730781961; pair (4052739537881, 6557470319842)

Sequential programs · Problem 0063

At Fibonacci iteration 62, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 62 begins with the pair of registers a=4052739537881, b=6557470319842.
  2. The current output is register a, so the emitted term is 4052739537881.
  3. Calculate a temporary sum t = a+b = 4052739537881+6557470319842 = 10610209857723.
  4. Copy the previous value of b into the new a register.
  5. The new a is 6557470319842.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 10610209857723.
  8. After the update, the pair is (6557470319842, 10610209857723).
  9. On the next iteration, the machine will emit 6557470319842.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 4052739537881; pair (6557470319842, 10610209857723)

Sequential programs · Problem 0064

At Fibonacci iteration 63, what is the output and next pair of register values?

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Iteration number 63 begins with the pair of registers a=6557470319842, b=10610209857723.
  2. The current output is register a, so the emitted term is 6557470319842.
  3. Calculate a temporary sum t = a+b = 6557470319842+10610209857723 = 17167680177565.
  4. Copy the previous value of b into the new a register.
  5. The new a is 10610209857723.
  6. Copy the computed temporary t into the new b register.
  7. The new b is 17167680177565.
  8. After the update, the pair is (10610209857723, 17167680177565).
  9. On the next iteration, the machine will emit 10610209857723.
  10. The ordering matters: updating a too early without a temporary could destroy a needed operand.
  11. This trace uses unlimited mathematical integers; an eight-bit real register would wrap far earlier.

Final answer: output 6557470319842; pair (10610209857723, 17167680177565)