---
title: "A Symbolic Analysis of Relay and Switching Circuits"
authors:
  - "Claude E. Shannon"
year: 1938
venue: "Transactions of the AIEE (MIT master's thesis 1937)"
arxiv: null
doi: "10.1109/T-AIEE.1938.5057767"
source: "https://doi.org/10.1109/T-AIEE.1938.5057767"
topics:
  - boolean-algebra
  - switching-theory
  - shannon
  - circuits
seed_rank: 552
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "systems"
relevance_score: 10
lineage: foundations-of-computing
cites:
  - title: "A Treatise on Universal Algebra"
    url: "https://archive.org/details/treatiseonuniver00whituoft"
    year: 1898
    arxiv: null
    doi: null
  - title: "The Algebra of Logic"
    url: "https://archive.org/details/algebbralogic00coutuoft"
    year: 1914
    arxiv: null
    doi: null
---

# A Symbolic Analysis of Relay and Switching Circuits

## One-sentence takeaway

Shannon shows that series-parallel relay networks are a physical model of Boolean algebra, so circuit design becomes algebraic simplification.

## Why it matters here

Every digital path in the Broadside engine — gates, masks, ECS enable bits — is the same correspondence Shannon made between hindering functions and propositional connectives.

## Key ideas

- A closed contact is 0 (no hindrance) and an open contact is 1; series combination is Boolean addition and parallel combination is multiplication.
- Any expression in the two-valued algebra can be realized by a relay network, and algebraic identities yield equivalent cheaper circuits.
- Hindrance functions are manipulated with Huntington's postulates; dual networks swap series/parallel and 0/1.
- Multi-terminal and sequential examples (adders, locks, interlocking) show the method is not limited to two-terminal combinational boxes.
- The 1937 MIT master's thesis, published in AIEE Transactions 1938, is the founding paper of switching theory.

## Caveats

## Links

- DOI: [10.1109/T-AIEE.1938.5057767](https://doi.org/10.1109/T-AIEE.1938.5057767)
- URL: https://doi.org/10.1109/T-AIEE.1938.5057767