PLC-Course

Sprint 2 Cheat Sheet — Digital Foundations

🔢 The Four Number Systems

System	Base	Digits	Where it shows up
Denary (decimal)	10	0–9	Human-readable values
Binary	2	0–1	Native to silicon, every bit in memory
Octal	8	0–7	Older Mitsubishi/Allen-Bradley I/O addresses
Hexadecimal	16	0–9, A–F	Memory addresses, data words
BCD	special	4 bits per decimal digit	Thumbwheel switches, 7-segment displays

⚡ Quick Conversion Reference

Decimal  Binary    Octal  Hex   BCD (per digit)
   0     0000        0     0     0000
   1     0001        1     1     0001
   2     0010        2     2     0010
   ...
   9     1001        11    9     1001
  10     1010        12    A     0001 0000
  15     1111        17    F     0001 0101
  16    10000        20   10     0001 0110
 173    10101101    255   AD     0001 0111 0011

🧠 Mental Tricks

Decimal → Binary: repeatedly divide by 2, write remainders bottom-up. Binary → Hex: group bits in 4s from the right, look up each nibble. Decimal → BCD: convert each decimal digit to 4 bits separately. 173 ≠ 10101101 in BCD; it’s 0001 0111 0011.

➖ Negative Numbers (Two’s Complement)

To represent -5 in 8-bit two’s complement:

1. Write +5 in binary: 0000 0101
2. Invert all bits: 1111 1010
3. Add 1: 1111 1011

Range of 8-bit signed: –128 to +127. Range of 16-bit signed: –32 768 to +32 767.

The MSB acts as a “sign bit” — 0 for positive, 1 for negative.

🧱 Word Sizes

Name	Bits	Range (unsigned)
Bit	1	0–1
Nibble	4	0–15
Byte	8	0–255
Word	16	0–65 535
Double word	32	0–4 294 967 295

🔌 I/O Addressing Across Vendors

A discrete input on terminal 0 of card 1:

Vendor	Notation	Example
Siemens (S7)	Ix.y	I0.0, I1.3
Allen-Bradley (Logix)	tag-based	Local:1:I.Data.0
Allen-Bradley (PLC-5/SLC)	I:s/b (octal!)	I:1/0, I:1/17 (= bit 15 decimal)
Mitsubishi	Xn (octal!)	X0, X10 (= 8 decimal)

⚠️ Octal trap: in older Allen-Bradley and Mitsubishi, the bit number jumps from 7 to 10, NOT 7 to 8. X10 is the 9th input, not the 11th.

🔄 I/O Update Strategies

Strategy	How	Pros	Cons
Mass I/O copy	Read all inputs at scan start, write all outputs at scan end	Deterministic, simple	Slight delay on output
Continuous update	Inputs/outputs accessed directly during scan	Lower latency for specific signals	Less deterministic, can race
Immediate I/O	Special instructions to bypass image table mid-scan	Fastest reaction	Only for critical signals

Most PLCs default to mass I/O copy; immediate I/O is reserved for safety-critical or fast-loop applications.

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