adder in logisim using only 2-input-NAND gates

Question

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

Answer 1

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:

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

Answer 2

Here is a half-adder using NAND gates:

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.