Nuts & Volts - June 2005

EXCELLENT CIRCUITS WITH EXCEL

Using Spreadsheets for Digital Circuits

BY PETER STARK

F o r

E l e c t r o n i c s

NUTS & VOLTS E v e r y t h i n g

Nuts & Volts Magazine recently had two articles about linear-feedback shift registers, which are shift registers with some of their outputs fed back to the input for generating cyclic redundancy check (CRC) bits or random numbers. Short of actually building these (and other digital) circuits, it’s sometimes hard to check that they do what they claim to do. Here is an interesting and simple technique for simulating these circuits on a computer using a spreadsheet program.

It doesn’t have to be an expensive or powerful spreadsheet program. For the examples below, I will use Excel, but sometimes old versions of Lotus 123 or shareware programs like As-Easy-As work even better.

The Inverter

Figure 1 shows the basic idea. Looking at an inverter — such as a 7404 — in the TTL manual, you’ll often see the inputs and outputs labelled as In and Out, or perhaps A

and B. But simply label them A1 and B1, and right away, you get the idea: Just use cell A1 in the spreadsheet for the input and cell B1 for the output. There’s nothing magic about these two cells, as you could use any two cells in the spreadsheet. Now all you have to do is put the right formula into cell B1, so it’s always the opposite of A1, and you’re done.

FIGURE 1. A simple inverter.

For the inverter in Figure 1, if the input is a 0, then the output is a 1, and if the input is 1, then the output is 0 (you have to use 0 and 1, because it won’t work if you try to use H and L or True and False instead). There are two ways to do this. The simplest is to write this as the simple formula:

Output = 1 - Input

In other words, in the spreadsheet, cell B1 should be equal to one minus whatever is in cell A1: 1 minus 0 is 1, whereas 1 minus 1 is 0. The formula then becomes:

B1 = 1 - A1

In Excel, you’d type =1-A1 into cell B1 (with the equal sign); whereas, in most other spreadsheets, it would be just 1-A1. Make sure to check the exact format for whichever spreadsheet you are using. Another way is to use the spreadsheet’s IF function, like this:

B1 = IF(A1 = 0, 1, 0)

The parentheses contain three arguments: a test, what to do if the test is correct, and what to do if it isn’t.

In this case, it says, “if A1=0, then make this cell equal to 1, otherwise make it 0.” For obvious reasons, I prefer to use the “one minus” approach.

Figure 2 shows some other simple gates, but let’s do them one at a time.

FIGURE 2. Simple digital gates.

The AND Gate

A1

B1

C1

0

1

0

1

0

1

TABLE 1

For the AND gate at the top left corner of Figure 2, the truth table (which describes how it works) is shown in Table 1, from which we can see that the output is just the product of the two inputs — a simple multiplication. So, the formula to put

into cell C1 is A1 x B1.

Some spreadsheets actually have functions for doing simple logical operations. Excel insists on using words like TRUE and FALSE, so that is not very useful to us, but 123 and others use ones and zeroes. The corresponding syntax for this formula in 123 and some others would be +A1#AND#B1. Don’t bother — A1 x B1 is much simpler.