Full Adder from Relays: Sum, Carry-In, and Carry-Out
In the previous post, we built the half adder: XOR for the sum bit, AND for the carry bit. Two inputs in, two outputs out — a clean circuit that correctly...
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Notes from the bench
Technical tutorials, teaching guidance, release notes, and analyses of the simulator’s implementation boundaries.
Relay Half Adder: Verifying Sum and Carry for Two Input Bits
In the previous post, we built a multiplexer that selects one of several signals. The half adder introduces a different interpretation of a Boolean output vector: two output bits jointly...
Multiplexer Explained: The Relay Circuit That Chooses Between Signals
In the previous post, we completed a survey of common two-input logic gates—AND, OR, NAND, NOR, XOR, and XNOR. Each applied one Boolean function to its inputs. Today...
XNOR Gate: Relay Equality Detection and Comparator Design
In the previous post, we built XOR from relays — the gate that asks are these two inputs different? It lit a lamp precisely when its inputs disagreed. That circuit is...
XOR Gate: The Difference Detector That Powers Binary Addition
In the previous post in this series, we explored the NOR gate and functional completeness: networks of NOR gates can implement any finite Boolean function. The same is true of...
NOR Gate with Relays: Universal Logic and the Apollo Guidance Computer
NOR is the complement of OR: It outputs 1 only when every input is 0. Like NAND, NOR is functionally complete: repeated NOR gates can express every finite Boolean function...
NAND Gate Explained: A Functionally Complete Boolean Primitive
NAND is the complement of AND. For two inputs: Its importance is mathematical: repeated NAND gates can express every finite Boolean function. This property is functional completeness. It does not...