01How Computers Work

Repetition with reasons, not memorization

Worked exercise library

2,686 fully worked problems across 10 categories. Every answer includes an explicit sequence of steps, from power-of-two place values through carries, overflow, memory addressing and loops.

How to use this collection

Choose a subject, attempt one question without peeking, and only then expand its full trace. These pages are an appendix, not required reading for the main 72-lesson journey.

Reading binary

Set 1

32 step-by-step problems with complete hidden solutions.

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Reading binary

Set 2

32 step-by-step problems with complete hidden solutions.

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Reading binary

Set 3

32 step-by-step problems with complete hidden solutions.

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Reading binary

Set 4

32 step-by-step problems with complete hidden solutions.

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Reading binary

Set 5

32 step-by-step problems with complete hidden solutions.

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Reading binary

Set 6

32 step-by-step problems with complete hidden solutions.

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Reading binary

Set 7

32 step-by-step problems with complete hidden solutions.

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Reading binary

Set 8

32 step-by-step problems with complete hidden solutions.

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Reading binary

Set 9

32 step-by-step problems with complete hidden solutions.

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Reading binary

Set 10

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 1

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 2

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 3

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 4

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 5

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 6

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 7

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 8

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 9

32 step-by-step problems with complete hidden solutions.

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Writing binary

Set 10

32 step-by-step problems with complete hidden solutions.

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Signed eight-bit values

Set 1

32 step-by-step problems with complete hidden solutions.

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Signed eight-bit values

Set 2

32 step-by-step problems with complete hidden solutions.

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Signed eight-bit values

Set 3

32 step-by-step problems with complete hidden solutions.

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Signed eight-bit values

Set 4

32 step-by-step problems with complete hidden solutions.

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Signed eight-bit values

Set 5

32 step-by-step problems with complete hidden solutions.

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Signed eight-bit values

Set 6

32 step-by-step problems with complete hidden solutions.

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Signed eight-bit values

Set 7

32 step-by-step problems with complete hidden solutions.

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Signed eight-bit values

Set 8

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 1

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 2

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 3

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 4

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 5

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 6

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 7

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 8

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 9

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 10

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 11

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 12

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 13

32 step-by-step problems with complete hidden solutions.

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Eight-bit addition

Set 14

4 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 1

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 2

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 3

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 4

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 5

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 6

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 7

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 8

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 9

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 10

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 11

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 12

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 13

32 step-by-step problems with complete hidden solutions.

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Eight-bit subtraction

Set 14

4 step-by-step problems with complete hidden solutions.

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Bitwise logic

Set 1

32 step-by-step problems with complete hidden solutions.

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Bitwise logic

Set 2

32 step-by-step problems with complete hidden solutions.

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Bitwise logic

Set 3

32 step-by-step problems with complete hidden solutions.

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Bitwise logic

Set 4

32 step-by-step problems with complete hidden solutions.

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Bitwise logic

Set 5

32 step-by-step problems with complete hidden solutions.

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Bitwise logic

Set 6

32 step-by-step problems with complete hidden solutions.

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Bitwise logic

Set 7

32 step-by-step problems with complete hidden solutions.

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Bitwise logic

Set 8

32 step-by-step problems with complete hidden solutions.

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Bitwise logic

Set 9

14 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 1

32 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 2

32 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 3

32 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 4

32 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 5

32 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 6

32 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 7

32 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 8

32 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 9

32 step-by-step problems with complete hidden solutions.

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ALU and condition flags

Set 10

12 step-by-step problems with complete hidden solutions.

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RAM addressing

Set 1

32 step-by-step problems with complete hidden solutions.

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RAM addressing

Set 2

32 step-by-step problems with complete hidden solutions.

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RAM addressing

Set 3

32 step-by-step problems with complete hidden solutions.

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RAM addressing

Set 4

32 step-by-step problems with complete hidden solutions.

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RAM addressing

Set 5

32 step-by-step problems with complete hidden solutions.

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RAM addressing

Set 6

20 step-by-step problems with complete hidden solutions.

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Branch and loop tracing

Set 1

32 step-by-step problems with complete hidden solutions.

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Branch and loop tracing

Set 2

32 step-by-step problems with complete hidden solutions.

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Branch and loop tracing

Set 3

32 step-by-step problems with complete hidden solutions.

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Branch and loop tracing

Set 4

24 step-by-step problems with complete hidden solutions.

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Fibonacci state traces

Set 1

32 step-by-step problems with complete hidden solutions.

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Fibonacci state traces

Set 2

32 step-by-step problems with complete hidden solutions.

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Fibonacci state traces

Set 3

16 step-by-step problems with complete hidden solutions.

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