Logic Gates & Boolean Algebra
Embedded → Digital Electronics
PrepFusion · Digital Electronics · Marathon 1
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Why this works · explanation & key points
Every digital signal is one of two levels: LOW (0) or HIGH (1). AND, OR, and NOT are the three primitives every other gate is built from.
Boolean laws exist to shrink your gate count
NOT(A AND B) = (NOT A) OR (NOT B) NOT(A OR B) = (NOT A) AND (NOT B)
Why this works · explanation & key points
Identity, idempotent, complement, absorption, and De Morgan's laws let you rewrite a gate network into an equivalent one with fewer gates — the same payoff whether minimizing an ASIC netlist or an interrupt-mask expression in firmware.
The bridge to C: bitwise operators ARE Boolean algebra
if (!(flag_a && flag_b)) and if (!flag_a || !flag_b)are De Morgan-equivalent. A compiler is free to emit either form's instruction sequence depending on optimization level — they compute the identical result. This is the direct C-language payoff of a law that looks purely academic on a truth table.flag_a = 0, flag_b = 0 !(flag_a && flag_b) → 1 !flag_a || !flag_b → 1 // same result — De Morgan holds
| a | b | !(a&&b) | !a||!b |
|---|---|---|---|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
Why this works · explanation & key points
A bitwise &, |, or ~ in C is this same Boolean algebra, executed across every bit lane of a register in one instruction — a debounce check or interrupt-mask test is a small gate network in software.
Toggle flag_a and flag_b — watch both expressions agree on every combination:
Practice
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