Binary Additions using Logic Gates

In our previous blog post “from transistors to processors” we found out that the CPU consists of logic gates, which are made using transistors.

In this blog post we are looking at how these logic gates can be combined to create an integrated circuit used by the ALU (Arithmetic and Logic Unit of the CPU) to add two 8-bits binary numbers together.

First let’s recap on how a binary addition works:

Half-Adder Circuit


A half-adder circuit is used to add two bits of data together and is based on the following Truth Table.
half-adder-truth-table

A half-adder circuit consists of two logic gates as follows:
Half-Adder

Full-Adder Circuit


A full-adder circuit is used to add three bits of data together and is based on the following Truth Table.
full-adder-truth-table

A full-adder circuit consists of two half-adder circuits and an OR gate connected as follows:
Full-Adder

Full Binary Addition


By connecting an half-adder circuit with 7 full-adder circuits we can create a circuit to implement a full binary addition of two 8-bits binary numbers:
Binary-addition-truth-table

Full circuit:
Binary-addition-using-binary-adder-circuits

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