HD70DigElec

Digital Electronics

Electrical Fundamentals: Buy a book and learn basic elements of electricity.

Ohms Law for DC Circuits (Battery source)
Known	I= Current	R=Resistance	E=Voltage	P=Power
I & R			E=I*R	P=I^2*R
I & E		R=E/I		P=E*I
I & P		R=P/I^2	E=P/I
R & E	I=E/R			P=E^2/R
R & P	I=(P/R)^1/2		E=(P*R)^1/2
E & P	P/E	E^2/P
Ohms Law for AC Circuits (Wall plug source)
Known	I= Current	Z=Impedance	E=Voltage	P=Power
I & Z			E=I*Z	P=I^2*Z cos θ
I & E		R=E/I		P=I*E cos θ
I & P		R=P/I^2cos θ	E=P/I cos θ
Z & E	I=E/Z			P=E^2cos θ/Z
Z & P	I=(P/Zcos θ)^1/2		E=(P*Z/cos θ)^1/2
Z & P	P/Ecos θ	E^2cos θ/P

I in amperes, R in ohms, Z in ohms, E in volts, P in watts, θ phase angle in degrees by which current leads voltage for capacitance and lags for inductance, L is Inductance in henries, C is capacitance in farads.

All persons should be exposed to the terms and relationships above. Everyone is in daily contact with these electrical terms and phenomenon.

Transistor Power Supply Regulation: One of the first application of transistors was for DC power supply regulation. There were may arrangements. These would soon be integrated into a single semiconductor. Capacitors remained the largest item, and still are though much smaller.

Early Logic Elements: During WW II logic circuits were made using telephone relays. Such were used to break codes, sometimes using entire buildings dedicated to such devices.

The first computers after WW II used vacuum tubes as the means to create logic elements. These were large racks of tube circuits; expensive, hot and prone to failure.

Discrete part Logic: Flip Flops were building blocks before integrated circuits.

When transistors first came out they were connected in a variety of ways to make families of logic elements as RTL= Resistor Transistor logic and DTL as Diode Transistor Logic. IBM used individual transistors plus resistors & diodes on 3”x4” plug in cards for each logic device. Because of all the hardware in the field, they were late in changing to the new dual inline IC Integrated Circuit packages.

Integrated Circuits: The bipolar TTL Transistor to Transistor Logic, family took off like wildfire and a short time later was superceded by CMOS Complementary Metal Oxide Semiconductor. TTL consumed power to sustain a given state. CMOS only consumed power during it’s change of state, and none when full ON of OFF. CMOS made it possible to make Microprocessors. CMOS was in it’s infancy in 1971, about two years after TTL had taken over the market.

NAND gates became building blocks for creating almost any kind of fixed logic. Boolean Algebra became a common way of defining what needed to be coupled to most economically build fixed logic. Then came the Set Reset Flip Flop. This evolved into a Clocked Flip Flop and soon an almost universal JK Flip Flop.

The JK flip flop could be interconnected to make Counters, Shift Registers, Data holding Latches. Soon these higher functional devices became available as building blocks and the earlier sets of logic became “glue” devices to interconnect the others.

Packaging: The flat pack became common for military applications and the dual inline packages standards for commercial applications.

Design layouts could be made as shown above right, with functions connected to pins. I made my designs using 1/8 grid paper drawing the inner connecting wiring – sometimes indicating chip-pin number for a connection. It worked better to place test probes on top view – and in time I could transpose the image of what function I was testing. Emil Kohler who was working with me would say how do you know that is the right pin? I’d chucked and said because I drew the underside so many times It’s hard to forget.

Binary in, 1 of 16 selected single out decoders for example were essential for timing a systems functions. These were a variety of kinds and arrangements. A most significant improvement was the Analog selector gate, this permitted passing information, not just presenting a 0 or 1 state.

Clock for Timing Functions: Thankfully I discovered in an RCA handbook how to make a clock I could adjust by selecting a resistor-capacitor combination that generated the desired frequency. Prior clocks for radio were generated by use of an Oscillator coil in association with a vacuum tube. Such could be replicated with transistors but had been dropped by the industry who were using crystals for timing clocks. These IC clocks as shown in the figure worked great.

Voltage to frequency Converters: For early experiments I found that multivibrator IC’s that had just come out to be very valuable. I was able to use these to convert a potentiometer voltage change to a frequency. I was able to make an X-Y variable resistor motion Joy Stick Pitch Yaw frequency output which when connected to a binary counter produced Pitch – Yaw binary commands.

Arithmetic Logic Units: The ALU was a godsend to the computing business. Prior to it’s arrival arithmetic was done by use of shifting “A” numbers and “B” numbers through a two bit adder and accumulate them in a “C” shift register.

The ALU could handle four two sets of four bits in parallel. They were also equipped with four function inputs that could tell the ALU what function to perform.

Look-ahead Carry: soon there was a companion Look-ahead carry chip that permitted automation of the carry process.

Logic Notations: you will notice the use of letters, some with lines above and some without. A line above means it’s a NOT function. If you take a look you will find that the output of flip flops are denoted as Q and Not Q. Q is used for output in lieu of O so as not to confuse it with Zero. The Q and Not Q indicate that what ever Q is the Not Q is the opposite, ie, it’s Not Q. For example if A = 1 then Not A = 0. if A =0 then Not A =1. A + B = A and B Unfortunately the symbol look up tables on this word processor do not include Boolean Algebra symbology.

Bits, Nibbles & Bites: It was soon necessary to develop standards and terms for dealing with binary numbers. A single item is called a “bit”, four bits is called a “nibble” and 8 bits is called a “bite”. It soon evolved that all early microprocessors and computing machines were based on 8 bits dealing with bites, often called bytes.

ASCII Code: The American Standard Code version II became the standard used for converting binary numbers to alpha numeric characters. This standard grew out of the telegraphy and telephone industry and is still used today. The 7 bit code covers standard alpha numeric figures. The full byte 8 bit set that follows includes additional characters. Some of the additional characters permit making block and flow diagrams using ASCII only. This was used extensively before Microsoft came up with the graphic interface with Windows which permitted use of custom made fonts as compared to standard byte character sets. Where as while I was working with these code the ASCII tables were available from many sources. Now I find they are hard to find because people no longer deal immediately with keyboard generated characters and no longer inspect memory direct.

Open Collector & Tri-state Logic: Initially the only way you could put multiple functions on line was to use Open Collector TTL devices where they all shared a single pull up resistor. A TTL logic device has a pull up resistor which caused the output to be high unless pulled low. If you are going to alternate outputs from one set of registers or memory devices onto a data bus, it was necessary to use special open collector devices and an independent set of pull up resistors. This was always a pain in the behind. With CMOS and the use of Transmission Gates it was possible to include Tri State logic on a device where it’s output was enabled or disabled from the bus.

Enable, Disable, Strobe, Clock, Select: With a tristate option IC came equipped with Enable, Disable, Strobe pins in addition to Clock and Select pins. This was very helpful in timing data trasfer. An input change of state could be enabled, sustained, clocked, held, then enabled; avoiding transient conditions being latched in a register. .

Binary, Hexi-decimal, 2s compliment and 1s compliment Numbers: Hexidecimal numbers permit dense display presentation of memory content. 1s or 2s compliment numbers are require when performing binary arithmetic.

Most significant binary bits at left, sign bit at far left.

Decimal	Hexi- decimal	Signed binary	2’s complement	1’s complement
15	F	01111	01111	01111
14	E	01110	01110	01110
13	D	01101	01101	01101
12	C	01100	01100	01100
11	B	01011	01011	01011
10	A	01010	01010	01010
9	9	01001	01001	01001
8	8	01000	01000	01000
7	7	00111	00111	00111
6	6	00110	00110	00110
5	5	00101	00101	00101
4	4	00100	00100	00100
3	3	00011	00011	00011
2	2	00010	00010	00010
1	1	00001	00001	00001
0	0	00000	00000	00000
				11111
-1	-1	10001	11111	11110
-2	-2	10010	11110	11101
-3	-3	10011	11101	11100
-4	-4	10100	11100	11011
-5	-5	10101	11011	11010
-6	-6	10110	11010	11001
-7	-7	10111	11001	11000
-8	-8	11000	11000	10111
-9	-9	11001	10111	10110
-10	-A	11010	10110	10101
-11	-B	11011	10101	10100
-12	-C	11100	10100	10011
-13	-D	11101	10011	10010
-14	-E	11110	10010	10001
-15	-F	11111	10001	10000

When viewing memory content it is very helpful to “compress” the display to maximize use of the limited confines of a monitor screen. Thus columns of Hex permit displaying binary in condensed form.

Hex	binary	binary
FF	1111	1111
EE	1110	1110
DD	1101	1101
CC	1100	1100
BB	1011	1011
AA	1010	1010
99	1001	1001
88	1000	1000
77	0111	0111
66	0110	0110
55	0101	0101
44	0100	0100
33	0011	0011
22	0010	0010
11	0001	0001
00	0000	0000

Binary Arithmetic: If you want to really understand how to do binary arithmetic, buy a book. It’s a very tedious process. The above diagram describes the algorithm used for multiply, which is a process of repeated additions per the principles of Booths Algorithm, below.

Above is the layout of a setup I created for scaling the servo actuator feedback signal and process sample data filtering. It took some time before I could figure out how to do this for a single multiply process, and much more time to handle a full set of servos and their shaping networks.