April 1972 Popular Electronics
Table of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
Popular Electronics,
published October 1954  April 1985. All copyrights are hereby acknowledged.

Whenever I read the April issue
of any magazine, vintage or contemporary, lurking in my mind is whether it is an attempt
at an April Fools "gotcha." The article title is usually the first clue that the author
is trying to punk me at least provides a sporting chance. Take for instance this "Analog
Logic" piece in the April 1972 edition of Popular Electronics. It could easily
be a hoax, so I proceeded cautiously. It turns out to be completely legitimate. James
Hannas provides a few examples of how analog circuits can be used to perform mathematical
functions that are easily handled by logic circuits. Of course prior to the introduction
of readily available, inexpensive digital integrated circuits only a few years earlier,
all those mathematical functions were performed by analog circuits, so this was nothing
new to most readers. If you have never researched the capabilities of both analog and
mechanical computers, it would be worth your time; you will be amazed. One example that
always impresses me is the
electromechanical systems that pointed and stabilized the massive gun turrets on
battleships during World War II.
Analog Logic: It Takes More Than FlipFlops to Make a Calculator
By James Hannas
Have you ever wondered how some complex calculators can do so many operations at such
high speed and accuracy? The answer is in the use of linear and nonlinear integrated
circuits that are basically quite simple in theory. Most of the circuits involve an operational
amplifier  a very highgain linear amplifier that inverts the input signal.
When input and feedback resistors are connected to the op amp as shown in Fig. 1,
the amplifier tries to maintain its input as close to zero as possible. The higher the
gain, the lower the offset or error voltage. To do this, the amplifier must cause a current
through the feedback and input so that the voltage drop across the input resistor is
equal to the input voltage. The input swing is equal to the input voltage times Rf/Ri.
A graphical analogy of the amplifier is shown in Fig. 2.
Using the same circuit, but with additional input resistors, the amplifier can be
made into an adder. The sum of the voltages can also be multiplied by a constant by adjusting
the input resistors.
Nonlinear functions, such as squaring, can be performed by the diode shunt matrix
shown in Fig. 3. By adjusting the feedback resistors, any type of curve with increasing
magnitude can be formed. A logarithmic, or decreasing, curve will result when the diode
matrix is used as a feedback instead of a shunt matrix.
The most common squaring circuit is shown in Fig. 4. The numbers on the op amps indicate
the multiplier constants. By adding one quarter of the sums of AB and A+B, the result
is the product of A and B.
Division is shown in Fig. 5. Here an op amp is supplied feedback by a multiplier circuit
which is controlled by B. As B increases, the output decreases.
There are also operational amplifiers and multipliers which are binarytoanalog and
analogtobinary converters. These are basically resistor networks and amplifiers. By
combining analog circuits with binary bit storage, switching and readouts, a compact
calculator can be designed.
Posted December 19, 2017
