5.5 Logic circuits Flashcards
Digital computers and Central Processing Units (CPUs) must be able to carry out arithmetic processes and logical combinations
These are done in an Arithmetic Logic Unit (ALU), the heart of each CPU.
a system that performs calculations or makes decisions is a logic system
A computer is a logic system that contains memory.
Computers and logic systems can handle either
analogue or digital information
The ALU needs its inputs in digital form such as:
Logic 1 (also known as logic ’True’)
Logic 0 (also known as logic ‘False’)
on/off or true/false in logic is defined as
1 and 0
1/0 in a logic system are known as binary digits abbreviated as
bits
a combination of bits is called a
word
two binary states can be represented in a variety of ways including
most common high and low voltage levels
also two different frequencies and two-phase angles
Positive logic is more commonly used where H means 1 and L means 0
.
Logic gate operations can be expressed using
Boolean Algebra
X = A or B and C
Truth tables specifically describe the
function of a logic gate
Logic gates have only three basic functions
- AND Function
- OR Function
- NOT (Inversion) Function
By combining the three basic functions
AND
OR
NOT
which others can be made
NAND (not AND)
NOR (not OR)
EXCLUSIVE OR
EXCLUSIVE NOR
There are several different ways to define logic functions
Circuit schematic/equivalent circuit
Logic symbol
Truth table
Signal diagram
NOT (inverter) Gate
an inverter has only one input, and its output is always the opposite of the input
- A = A A - logic 0: produces 1 A - logic 1: produces 0
AND Gate
both relays need to be energised (logic 1 inputs) to give a logic 1 output.
AND and OR gates are usually what
Transistors
AND Gate
X = A . B
the . is read as AND
NAND Gate
X = NOT A and B
NOT bubble at the output inverts the output of the AND gate making it a NAND.
NAND Gate truth table
The output is a logic 1 when any input is 0.
The output is a logic 0 only when all inputs are 1.
OR Gate
either relay needs to be energised (logic 1 inputs) to give a logic 1 output. These relays will be transistors.
the + sign means what in logic circuits
OR
NOR Gate
the output is inverted (NOT OR)
A NOR gate (Not OR) has two or more inputs and one output
NOR Gate truth table
X = NOT A or B
The output is only a logic 1 if all inputs are at logic 0
what’s the difference between a NAND and NOR gate
The NOR gate is a gate that produces a logic 1 output only when all of its inputs are logic 0.
The NAND gate is a gate that produces a logic 1 output only when one or more of its inputs are logic 0
XOR (exclusive OR)
Some circuits are required to perform only when either input is 1, not both. They will only output a 1 when the inputs are not identical. These are called XOR gates
AKA EXOR
⊕ this symbol is called the
XOR operator
XNOR (exclusive NOR)
Has two inputs and one output
outputs are the inverse of the XOR gate
XNOR truth table
The output is at logic 0 when input A is at logic 1 and input B is at logic 0, or vice versa.
The output is at logic 1 when both inputs A and B are at logic 1, or both inputs are at logic 0.
Inverters
Inverters have one input and one output. The output will produce the complement (opposite) of the input
when are inverters used
they are used when the complement of a particular signal is required within a logic circuit
what does a small circle at the input indicate
indicates that a logic “zero” will now activate the element at that particular input
INHIBIT Gate
Occasionally if required to “hold” one input to an “AND” gate at a particular logic level to disable the entire gate
The inhibit is logic 1 to disable the gate. The inhibit at logic 0 enables the gate
what is a full adder derived from
two half adders and an OR gate
