What are the basic building blocks of combinational logic circuits? In this lecture, 1
I am going to introduce you to logic gates that can be used to build any combinational circuits. 2
Although designing with these gates is not the goal of HLS, understanding their behaviour and functionality 3
helps us to develop an optimum design in HLS. 4
Logic gates are fundamental building blocks of combinational circuits. There are three basic logic 5
gates: AND, OR and NOT. The output of an AND gate is one if and only if both inputs are 1. The output 6
of an OR gate is one 7
if at least one of the inputs is 1. The NOT gate reverses the state of its input. 8
The combination of an AND and NOT gates is called NAND gate. Also, the combination of an OR and 9
NOT gates is called NOR gate. 10
These gates are important because any complex combinational circuits can be built by using only one 11
of them. 12
Therefore, they are called functionally complete gates. 13
Also, in some semiconductor technologies manufacturing these gates are easier than basic logic gates. 14
Exclusive-OR, or XOR for short, is another gate that can be built by using basic logic gates or by using 15
functionally complete gates. The output of an exclusive-OR gate is one if and only if exactly one of 16
its inputs is one. 17
In other words, if the inputs are not equal. The last special gate is called XNOR, 18
that is the negative of XOR. The output of this gate is one 19
if and only if the inputs have the same value. 20
In other words, the inputs are equal. 21
Let’s see an example designed by these gates. Single bit binary adder is one of the simplest combinational 22
circuits. 23
This adder receives two binary inputs and generates two binary outputs, representing sum and carry bits. 24
This circuit can be built using XOR and AND gates. 25
This circuit is also called half-adder. 26
The truth table represents the functionality of this design. 27
However, to extend this addition to more than one bit, we should involve the carry bit, as an input. 28
The resulted adder is called the full adder, which is a single-bit binary adder that receives a third input 29
as the carry generated by the predecessor bit. 30
This figure shows the full adder digital circuit and its corresponding truth table. 31
Real logic gates cannot react immediately to the input changes. 32
So, what is a delay of a gate or a logic circuit to possible changes on the input values? 33
The next lecture covers the concept of delay in logic circuits. 34
These are the takeaway messages. All combinational logic functions can be implemented by three basic 35
gates AND, OR, NOT, NAND or NOR gates are enough to implement any combinational logic circuit. 36
Now the quiz for this lecture. Show these equivalencies also known as De Morgan’s laws.