Digital Logic, Static and Dynamic Digital Systems
Digital Logic = the way electronic circuits process information using 2 states:
0 — usually represents a low voltage or “off” state
1 — usually represents a high voltage or “on” state
bit = a single binary digit
Logic gates
Truth tables
A truth table lists every possible input combination and the output.
AND gate
A | B | A AND B |
|---|---|---|
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
OR gate
A | B | A OR B |
|---|---|---|
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 1 |
NOT gate
A | B |
|---|---|
0 | 1 |
1 | 0 |
Combinational logic: static systems
A combinational circuit produces its output from its current inputs. It has no memory of previous inputs.
Examples include:
Adders
Multiplexers
Decoders
Comparators
Logic used in an ALU
For a combinational system:
Output = function of current input
If the inputs change, the output changes after a small circuit delay.
Sequential logic: dynamic systems
A sequential circuit can store information. Its output depends on the current inputs and the system’s previous state.
Sequential circuits commonly use:
Latches or flip-flops to store bits
A clock signal to coordinate when state changes
Feedback, where an earlier output affects later behaviour
Examples include:
Registers
Counters
Memory circuits
State machines
For a sequential system:
Next state = function of current input and current state
A clocked circuit typically updates its stored state at a clock edge. This allows different parts of a digital system to work in a coordinated sequence.
Static versus dynamic
Here, static refers to logic whose output is determined by the present inputs, while dynamic refers to systems whose behaviour changes over time and can depend on stored state.
Combinational / static | Sequential / dynamic |
|---|---|
No stored state | Stores state |
Output depends on current inputs | Output depends on inputs and previous state |
Example: AND gate or adder | Example: register or counter |
How logic builds a computer
Logic gates can be combined into larger circuits:
Gates form circuits such as adders and comparators.
These circuits form components such as an ALU or register.
Components combine to build a CPU, memory and other computer systems.
For example, an adder combines logic gates to calculate the binary sum of two values. The CPU’s ALU uses circuits like this when executing arithmetic instructions.
Key terms to remember
Bit · binary · logic gate · truth table · combinational circuit · sequential circuit · state · flip-flop · clock · feedback
Check your understanding
What is the output of
1 AND 0?What is the output of
1 XOR 0?Why does a sequential circuit need memory or state?
Is an adder usually combinational or sequential?
Is a register usually combinational or sequential?
Answers:
0
1
its output or next state can depend on what happened previously
combinational
sequential, because it stores a value