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I want to build an adder in logisim only with 2-input-NAND gates. The adder consists of 2 inputs (1 x constant 1 and 1 x arbitrary number) and an output.

The first thing which came into my mind is a 8-bit full adder but maybe there is an easier solution for this (because of the constant 1). Has anyone an idea? THX

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  • $\begingroup$ It's slightly unclear what you're asking for. NAND is boolean-complete, so you can build any other gate using just NANDs. Do you just want a full adder / half adder? $\endgroup$ – Ben I. Apr 23 '17 at 22:35
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If I understand your question right, you want to build an incrementor.

First you need to build a halfadder. If you do not can or want to design it, you can ask logisim to do it.

choose project/analyse circuit. add two inputs (a,b) and two outputs (o,c).

then fill in the logic table for the half adder.

a b | o c
...............
0 0 | 0 0
0 1 | 1 0
1 0 | 1 0
1 1 | 0 1

then push build circuit and check both options (2 input gates only and nand only)

logisim wil build the circuit:

enter image description here

then you can connect 8 halfadders to build a 8 bits incrementor.

enter image description here

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Here is a half-adder using NAND gates:

enter image description here

The way it works is by imitating an and gate on the bottom and an xor gate on the top. The trickiest part of understanding the diagram, I think, is the idea of putting the same input twice into a nand (such as just before the Sum output). When you stick two of the same input into a nand gate, you reduce yourself to two input possibilities: 1, 1, and 0, 0. This causes NAND to behave as a not gate.

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