555

Do you mean the number 555 (math) or the 555 timer integrated circuit (electronics) for your exam prep? I can help with either. Here are quick starters for both:

If you mean 555 (math):

• Prime factorization: 555 = 3 × 5 × 37
• Divisors: 1, 3, 5, 15, 37, 111, 185, 555 (eight divisors)
• Sum of divisors (including itself): 912
• Proper divisors sum: 912 − 555 = 357
• Parity: odd
• Digits sum: 5+5+5 = 15
• Base conversions: binary 1000101011, hex 0x22B, Roman numeral DLV
• Divisible by: 3 and 5 (and thus by 15)
• Quick problem you might see: find the number of divisors, or compute sigma(555)

If you mean 555 timer (electronics):

• Pins and basic modes: Reset, Control, Trigger, Threshold, Discharge, Output, Vcc, GND
• How it works: internal comparators compare the timing capacitor voltage to 1/3 Vcc and 2/3 Vcc; a flip-flop controls the discharge transistor to create oscillation or a pulse
• Astable mode (free-running oscillator):
  • t_high = 0.693 (RA + RB) C
  • t_low = 0.693 RB C
  • Frequency f = 1.44 / [(RA + 2RB) C]
  • Common values: RA, RB in kΩ, C in F
• Monostable mode (one-shot):
  • Pulse width t = 1.1 R C
  • Triggered when input goes below 1/3 Vcc; output goes high until capacitor charges to 2/3 Vcc
• Example: RA = 10kΩ, RB = 20kΩ, C = 100 nF
  • f ≈ 1.44 / [(10k + 2×20k) × 100nF] = 1.44 / (50k × 100nF) ≈ 288 Hz

Would you like:

• a focused set of practice problems (math or electronics) with solutions, or
• a deeper walkthrough of a specific topic (e.g., modular arithmetic with 555, or designing a 555 astable circuit),
• or a quick memorization cheat sheet for the topic you’re studying?