Binary Course

21 lessons. Sign in to keep track of your progress.

1. Part A — Counting in other bases
2. 1. Why Computers Don't Count in Decimal
3. 2. Binary: Place Value With Only Two Digits
4. 3. Hex: Binary in Groups of Four
5. 4. Converting Between Binary, Hex, and Decimal by Hand
6. Part B — Bitwise operations
7. 5. AND, OR, XOR, NOT: Bit-by-Bit Logic
8. 6. Shifts: Moving Bits Left and Right
9. 7. Masking: Reading and Writing Just the Bits You Care About
10. 8. Packing Multiple Fields Into One Word
11. Part C — Negative numbers
12. 9. Sign-Magnitude, and Its Awkward Downside
13. 10. One's Complement, Briefly, and Why It Was Mostly Abandoned
14. 11. Two's Complement: The Trick, and Why It Actually Works
15. 12. Two's Complement Arithmetic: Subtraction Without a Subtract Circuit
16. 13. Overflow: When the Answer Doesn't Fit
17. Part D — Fractions in binary
18. 14. Place Value Past the Point
19. 15. Converting Decimal Fractions to Binary (And Why Some Never Terminate)
20. 16. Fixed-Point: Tracking Your Own Binary Point By Hand
21. 17. Scaled Fixed-Point in the Wild: A Historical Survey
22. Part E — Reading real machine words
23. 18. A Word Is Just Bits, Until You Decide What It Means
24. 19. Worked Example: Decoding a Raw Word From the LGP-30
25. 20. Practice Set: Mystery Dumps, Mixed Bases and Interpretations
26. 21. Where to Go Next