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Objectives. At the end of the course you should. Be able to design and construct simple digital electronic systems. Be able to understand and apply Boolean logic and algebra – a core competence in Computer Science. Be able to understand and build state machines.
Introduction to Logic Gates. We will introduce Boolean algebra and logic gates. • Logic gates are the building blocks of digital circuits. Logic Variables. Different names for the same thing. Logic variables. Binary variables. Boolean variables. Can only take on 2 values, e.g., TRUE or False. ON or OFF. 1 or 0. Logic Variables.
The outputs of the gates assume at all times the value of the Boolean function, implemented by the circuit. In contrast, a dynamic circuit relies on temporary storage of signal values on the capacitance of high impedance circuit nodes.
Some of the important digital ICs are shown in Figs. 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7 and 2.8. A combinational circuit is one whose output at any time is based only on the present combination of inputs at that point of time. This chapter focus on logic gates and combinational logic circuits.
What is a combinational circuit? What are the inputs and outputs of a combinational circuit? What does a combinational circuit achieve? What are the different ways of representing combinational circuits? Why is the role of Boolean Algebra in designing combinational circuits? gning a combinational ci. What is a combinational circuit? No memory.
A combinational logic expression is a mathematical formula which is to be interpreted using the laws of Boolean algebra: given the expression a + b, for example, we can compute its truth value for any given values of a and b; we can also evaluate relationships such as a + b = c. A logic gate computes a specific Boolean function, such as (a + b)’.
The basic logic gates are the inverter (or NOT gate), the AND gate, the OR gate and the exclusive-OR gate (XOR). If you put an inverter in front of the AND gate, you get the NAND gate etc. One of the common tool in specifying a gate function is the truth table.
