555

Do you mean one of these?

• Math: the number 555 (properties, factorization, etc.)
• Electronics: the 555 timer IC (how it works and formulas for astable/monostable modes)

If you want, I can tailor it to your course. In the meantime, here are quick notes for both:

Math (555 as a number)

• Factorization: 555 = 3 × 5 × 37
• Divisors: 1, 3, 5, 15, 37, 111, 185, 555
• Sum of divisors σ(555) = (1+3)(1+5)(1+37) = 4 × 6 × 38 = 912
• Number of divisors: 8
• Base representations:
  • Binary: 555 = 1000101011₂
  • Decimal digits sum = 5+5+5 = 15 → digital root 6
• Modulo checks: 555 ≡ 6 (mod 9); 555 ≡ 5 (mod 11)

Electronics (555 timer IC)

• Pinout (common 8-pin DIP): 1 GND, 2 Trigger, 3 Output, 4 Reset, 5 Control, 6 Threshold, 7 Discharge, 8 Vcc
• How it works: internal comparators compare the capacitor voltage to 1/3 Vcc and 2/3 Vcc; a flip-flop drives the output and discharge transistor.
• Astable mode (free-running oscillator):
  • Frequency: f ≈ 1.44 / [(R1 + 2R2) C]
  • Duty cycle: D ≈ (R1 + R2) / (R1 + 2R2)
  • t_high ≈ 0.693 (R1 + R2) C; t_low ≈ 0.693 R2 C
• Monostable mode (one-shot):
  • Pulse width: t ≈ 1.1 R C
• Typical uses: timers, PWM, pulse generation, simple oscillators.

Would you like:

• A few exam-style practice problems with solutions for math or for the 555 timer?
• A deeper dive into a specific topic (e.g., factorization and divisors, or deriving the timing equations for the 555)?