stibitz.adder

From: Eric Smith <eric_at_brouhaha.com>
Date: Tue Apr 11 23:25:05 2000

> have I constructed a 1-bit binary adder or a 2-bit binary adder?

1-bit. A 2-bit adder has three bits of output and handles six more cases:

01 + 11 = 100
10 + 10 = 100
10 + 11 = 101
11 + 01 = 100
11 + 10 = 101
11 + 11 = 110

However, it still sounds like fun!

Logically a 2-bit adder can be decomposed into two one-bit full adders,
each with the following truth table:

A B Cin Cout Q
-------- ------
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1

The least significant stage of the mutli-bit adder can be simpler since
there is (usually) no carry-in:

A B Cout Q
---- ------
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 0

This is exactly what George Stibitz's Model K does.
Note that this can be implemented with no relays if
the inputs are only from switches (not the outputs of
other circuits), by using three-pole double-throw switches.
(I'm not going to try to draw ascii art unless someone
requests it.)

So an interesting challenge would be to minimize the
circuit for the full adder, given that the A and B
inputs are from switches, but the C input is an
electrical input from the lower-order stage.

I think at least one relay is needed, to act as an
inverter for the carry-in stage.

Eric
Received on Tue Apr 11 2000 - 23:25:05 BST