Course

Digital Logic Design: from gates to machines that remember

Name: Digital Logic Design: from gates to machines that remember
Price: 1999 BDT

Build circuits from the gate up, then give them memory. Simplify with Karnaugh maps, wire an adder, watch two gates hold a bit, and design a machine that finds a pattern. Follows the first digital logic course at universities such as NSU (CSE231) and BRAC (CSE260).

46 lessons4h 17mEnglish

What you'll learn

Convert between binary, decimal and hexadecimal by place value and by grouping bits
Read 4-bit two’s complement values, subtract by adding the negation, and recognise overflow
Read and write the truth table of any expression in AND, OR, NOT and XOR
Prove De Morgan’s laws from truth tables, and build AND and OR from NAND alone
Simplify a function of up to four variables with a Karnaugh map, using don’t-cares where they exist
Design a full adder, a multiplexer and a decoder from basic gates
Explain why a latch can give different outputs for the same inputs
Draw Q for a D latch and a D flip-flop from the same clock and data waveforms
Explain what a JK flip-flop does with both inputs high, and use a T flip-flop as a divider
Design the reset logic that makes a counter of any length up to 16
Trace bits through a shift register and load a chosen pattern into it
Build Moore and Mealy sequence detectors from the pattern they must find, with their backward transitions
Power and wire a 74-series chip from its pinout, and diagnose the common wiring faults

Requirements

No electronics background. The course starts from gates and never opens one up
Digital Electronics is the course before this one if you want to see what is inside a gate; it is not required
Comfort with powers of two helps in chapters 1 and 6

Course content

46 lessons · 4h 17m

Numbers a circuit can hold

A wire can only be high or low, so every number a circuit handles is written in base 2. Read binary by place value, compress it into hexadecimal, and watch four bits become a digit on a display.

0/6

Place value in base 2

Each place is worth twice the place to its right, so four bits hold every number from 0 to 15.

Preview6m 2.

Four bits make one hex digit

Sixteen values fit in four bits, so hexadecimal is binary written in groups of four.

Preview6m

Four bits on a display

A seven-segment display is driven by logic that turns four bits into seven lamps.

Negative numbers without a minus sign

Call the top half of the 4-bit patterns negative, and 7 + 1 overflows to −8.

Subtraction on the same adder

Invert and add one gives the negative, so a processor subtracts by adding.

Chapter check: binary, hex and negative numbers

Four questions on place value, hex grouping, what four bits can hold, and overflow.

Gates and Boolean algebra

A gate is a rule for one output, and an expression is a way of writing that rule. Read gates from their truth tables, prove De Morgan’s laws by comparing two tables, and build every gate you need from NAND alone.

0/5

Three gates and their tables

AND, OR and XOR differ on exactly one row of the table, and that row is worth predicting.

Preview6m 2.

An expression is a table

Any Boolean expression has exactly one truth table, found by working through every input row.

Preview7m

De Morgan: two expressions, one table

Two expressions are equal when their truth tables match on every row, which is how De Morgan’s laws are proved.

One gate builds the rest

NAND alone can make NOT, AND and OR, so a whole computer can be built from one kind of gate.

Chapter check: gates and Boolean algebra

Three questions on gate tables, De Morgan’s laws and universal gates.

Fewer gates for the same job

Two circuits with the same truth table do the same job, so the cheaper one wins. A Karnaugh map lays the table out so that simplifications become shapes you can circle, including the ones hidden across its edges.

0/4

A table folded into a map

Neighbouring cells differ in one input only, so a group of neighbours cancels that input out.

Preview7m 2.

Groups across the edge

The map wraps around, so the four corners are neighbours and can form one group.

Preview7m

Inputs that never happen

When some input rows can never occur, you may treat them as 1 or 0, whichever makes the groups bigger.

Chapter check: Karnaugh maps

Three questions on adjacency, wrap-around groups and don’t-cares.

Circuits that calculate

Gates arranged with a purpose become the building blocks of a processor. Add two bits, then three, then build the adder yourself, and finish with the two circuits that choose and decode: the multiplexer and the decoder.

0/6

Adding two bits

One plus one is 10 in binary, so adding two bits needs two outputs: a sum and a carry.

Preview6m 2.

The carry from the column before

Every column after the first adds three bits, because it must include the carry from its right.

Preview7m

Build a full adder

Two half adders and an OR gate make a full adder, and chaining full adders adds numbers of any length.

A switch made of gates

A multiplexer passes one of two inputs to its output, chosen by a select line.

One output line per number

A decoder turns a binary number into exactly one high output line out of many.

Chapter check: combinational circuits

Three questions on adders, multiplexers and decoders.

Circuits that remember

Every circuit so far gave the same output for the same inputs. Cross two gates so each feeds the other, and that stops being true: the circuit starts to remember. Then learn exactly when a latch and a flip-flop read their input.

0/7

Same inputs, different output

Two NOR gates feeding each other can hold a 1 or a 0 with exactly the same inputs.

Preview7m 2.

The input you must not use

Releasing S and R together from both high leaves two identical gates with no way to decide.

Preview7m

When does it look at D?

A latch reads D the whole time the clock is high; a flip-flop reads it only at the rising edge.

Change D while the clock is low

The two circuits agree exactly when D never changes during a clock-high window.

What to do with both inputs high

The JK flip-flop gives the forbidden input a use: both high toggles Q at the edge.

The T flip-flop, a divider by two

Tie K to J and Q flips on every edge, which halves the clock frequency.

Chapter check: latches and flip-flops

Four questions on memory, the forbidden input, edge triggering and the JK flip-flop.

Counters and state machines

Put flip-flops together and they can count, divide a frequency, and follow rules. Build a counter that stops at any number, then design a state machine that watches a stream of bits for a pattern of your choosing.

0/7

Counting is dividing

Each bit of a counter changes half as often as the one before, so a counter is also a frequency divider.

Preview7m 2.

Stop at nine

One gate that recognises the last count, and resets on the next edge, makes a counter of any length.

Preview7m

A stream in, a word out

A shift register collects bits sent one at a time and presents them all at once, in reverse order.

A machine that finds a pattern

Each state remembers how much of the pattern the latest bits match, and the output lives in the last state.

Where a wrong bit lands

A wrong bit does not always send the machine back to the start, because part of what it saw may still be useful.

A machine with one state fewer

A Mealy machine puts its output on the arrow, so the same detector needs one state fewer.

Chapter check: counters and state machines

Five questions on frequency division, mod-N reset logic, shift registers and state machines.

On the bench

The lab session of this course is spent wiring real 74-series chips, and first circuits fail on wiring, not on logic. Power a chip, count its pins from the notch, and build a function that needs two gates from one chip.

0/4

Power first

A chip is powered through pin 14 and pin 7, not through its inputs, and without that nothing works.

Preview7m 2.

Reading a pinout

Pins are counted from the notch, and chips that look alike can put their outputs in different places.

Preview7m

Two gates, one chip

A jumper from one gate’s output to another gate’s inputs builds AND from a NAND chip alone.

Chapter check: on the bench

Three questions on power pins, pinouts and the faults that stop a circuit working.

About the creator

Classytic