Code: Logic with Switches

In one line: George Boole turned logic into algebra, and switches do that algebra with electricity — series is AND, parallel is OR.

Companion to: Charles Petzold, Code (2nd edition), chapter 6.

Boolean algebra

George Boole (1850s) treated logic like arithmetic on sets and true/false values.

Operation	Meaning	Set view	Boolean arithmetic
AND	Both must be true	Intersection	Like × (1 × 1 = 1, anything × 0 = 0)
OR	Either can be true	Union	Like + (but 1 + 1 = 1)
NOT	Flip it	Everything outside the set	1 − x

Example condition: “a cat that’s female AND neutered AND (black OR white) AND NOT tan”. Parentheses matter exactly as in arithmetic.

Switches do logic

AND — series: both must be closed      OR — parallel: either closed is enough

 +──[A]──[B]──(bulb)──┐                 +──┬──[A]──┬──(bulb)──┐
                      │                    └──[B]──┘          │
 −────────────────────┘                 −─────────────────────┘

A	B	Series (AND)	Parallel (OR)
off	off	dark	dark
off	on	dark	lit
on	off	dark	lit
on	on	lit	lit

The same logic in every tool

Tool	AND	OR	NOT
PowerShell	`-and`	`-or`	`-not` / `!`
Python	`and`	`or`	`not`
Bash	`&&`	`\|\|`	`!`
SQL	`AND`	`OR`	`NOT`
JavaScript / C	`&&`	`\|\|`	`!`
Bitwise (numbers)	`&`	`\|`	`~`

Get-Service | Where-Object { $_.Status -eq 'Running' -and $_.StartType -eq 'Manual' }

SELECT * FROM logins WHERE (result = 'fail' OR locked = 1) AND NOT user LIKE 'svc_%';

🔐 Security and IT connections

Firewall rules, SIEM queries, group policies and search filters are all Boolean expressions. A misplaced OR can let everything through; a missing parenthesis can change the meaning completely.
Detection example (KQL): SecurityEvent | where EventID == 4625 and not(Account has "svc_") finds failed logons, excluding service accounts.
Test logic with a truth table before trusting a complex rule.

Practice drills

1. Two switches in series: A on, B off. Is the bulb lit?

No — series is AND, so both must be on.

2. Write "running services that aren't Automatic" in PowerShell.

Get-Service | Where-Object { $_.Status -eq 'Running' -and $_.StartType -ne 'Automatic' }

3. In Boolean arithmetic, what's 1 + 1 for OR?

1 — OR is true if either input is true, and there’s nothing “more true” than true.

Key takeaways

Boolean algebra: AND (intersection, ×), OR (union, +), NOT (complement).
Switches in series = AND; in parallel = OR.
The same three operators run every query, filter and rule you’ll write.