Electronic circuits to perform standard software operations

logic gates, including AND, OR, NOT, NAND, NOR, XOR

  • Logic gates are hardware circuits that produce a 1 or 0 output signal depending if the input requirements are satisfied. They are usually implemented in the computer using integrated circuits; a small silicon chip containing components such as resistors, diodes, transistors, and capacitors.

Type of logic gates shown in table below. Standard gates are AND,OR and NOT … NAND and NOR can be created using combination of AND+NOT and OR+NOT

truth tables

  • Truth tables are a compact way of showing the possible outputs from all possible variations of inputs into a logic gate.

circuit design steps

  • Designing a circuit to perform a particular function requires a systematic procedure:
  1. Identify inputs and outputs: Determine the number of inputs and outputs needed.
  2. Identify required components: Determine which logic gates are needed.
  3. Check the solution with a truth table: Test whether the solution works as required.
  4. Evaluate the circuit design: Ensure circuit is efficient, and meets design criteria.

specialty circuits:

  • All circuits are made from a combination of the basic logic gates, and can be designed to perform addition, subtraction, and comparisons. As the number of inputs increases, circuits become more complex.
  • Combinational circuits(for example Adders) produce instant output.
  • Sequential circuits(for example flip-flops) contain memory cells and logic gates, and the memory state is determined by previous inputs.

ADDERS

  • When two single digits (ones) are added, the result consists of two digits, 10 (or in decimal form, 2). This is called a SUM and acarry.
  • A half adder is a combinational circuit made by combining the AND and XOR gates allowing for the addition of two bits. It has two inputs (the two bits) and two outputs (Sum and Carry). It is limited because it can’t use the carry from a previous adder circuit.
  • A full adder is a combinational circuit made by combining two half adders and introducing an OR gate. It has three inputs (two bits to add, plus carry bit from another addition). Full adder has two outputs (Sum and Carry). It has the advantage that it can accept a carry bit from a previous addition.
  • Manny adders can be combined to perform arithmetic inside computer. For example, 8 full adders can add 8 bits of data – or a single Byte.

FLIP-FLOPS

  • A flip flop is a circuit that can store a binary value (1 or 0) as long as power is supplied. When a value has been sent, it remains in this state until told to change. They can be made from a combination of NAND or NOR gates. They have two inputs, Set and Reset (S and R), and two outputs, Q and Q’.
  • Flip flops are the basic building blocks of computer memory.
  • NAND and NOR flip flops establish a state of 1 when one 0 input and one 1 input are sent into the Set and Reset. Sending in two 1 inputs gives no result, and it is impossible to send in two 0 inputs (ie, computers are deliberately wired up so this won’t happen). As a result, and output has been set up so that future input can determine what value is stored.

Below is an example of a NAND flip-flop. Flip flops can also be made using NOR structures.

PAST HSC QUESTIONS

(i) Describe the function of a flip-flop, and briefly explain how it achieves

its purpose. You may use a diagram to illustrate your answer.

SYLABUS ITEMS COVERED

Students learn about: / Students learn to:
Electronic circuits to perform standard software operations
•logic gates, including:
–AND, OR, NOT, NAND, NOR, XOR
•truth tables
•circuit design steps
–identify inputs and outputs
–identify required components
–check solution with a truth table
–evaluate the circuit design
•specialty circuits, including:
–half adder
–full adder
–flip-flops as a memory store / •generate truth tables for a given circuit
•describe the purpose of a circuit from its truth table
•design a circuit to solve a given problem and use a truth table to verify the design
•explain how a flip-flop can be used in the storage and shifting of a bit in memory
•build and test a circuit using integrated circuits or use a software package
•simulate the testing of a circuit for both user-designed circuits and the specialty circuits
•recognise the cyclical approach to circuit design
•modify an existing circuit design to reflect changed requirements