Lecture 08 - Combinational Logic Circuits PDF

Combinational Logic Circuits Lecture 8  Design Methods Type of IC chips (based on packing density) : Small-scale integration (SSI): up to 12 gates Medium-scale integration (MSI): 12-99 gates Large-scale integration (LSI): 100-9999 gates Very large-scale integr...

Combinational Logic Circuits Lecture 8  Design Methods Type of IC chips (based on packing density) : Small-scale integration (SSI): up to 12 gates Medium-scale integration (MSI): 12-99 gates Large-scale integration (LSI): 100-9999 gates Very large-scale integration (VLSI): 10,000-99,999 gates Ultra large-scale integration (ULSI): > 100,000 gates  Design Methods Main objectives of circuit design: 1. Reduce cost - reduce number of gates - reduce IC packages 2. Increase speed 3. Design simplicity (reuse blocks where possible)  Logic circuits 1. Combinational 2. Sequential Outputs depend only on the current inputs. Outputs depend on the current inputs and previous inputs. Examples: Examples: Encoder Flip-flops Decoder Adders Subtracters Counters Multiplexer Demultiplexer Registers Clocks  Logic circuits 1. Combinational 2. Sequential  Combinational Sequential In this output depends only upon present input. In this output depends upon present as well as past input. Speed is fast. Speed is slow. It is designed tough as compared to combinational It is designed easy. circuits. There is no feedback between input and output. There exists a feedback path between input and output. This is time independent. This is time dependent. Elementary building blocks: Logic gates Elementary building blocks: Flip-flops Used for arithmetic as well as boolean operations. Mainly used for storing data. Don’t have capability to store any state. Have capability to store any state or to retain earlier state. These circuits do not have any memory element. These circuits have memory element. It is easy to use and handle. It is not easy to use and handle. Applications of Combinational LogicCircuits Calculators Digital measuring techniques Computers Digital processing Automatic control of machines Industrial processing Digital communications Design Combinational LogicCircuits Steps 1. Identify Problem from Verbal Description. 2. Specify the number of inputs and required numbers of outputs and assign symbols. 3. Construct the truth table to define relationship between inputs and outputs. 4. Simplify Boolean function using K-Map or Boolean Algebra rules. 5. Draw logic diagram for the simplified logic expression. Q: Design combinational logic circuitfor the below scenario A committee of three individuals decide proposal for an organization. Each individual votes either yes or no for each proposal that arises. A proposal is passed if it receives at least two yes votes. Design a circuit that determines whether a proposal passes. Solution Three inputs (x, y, z) – Individual votes One Output (F) – Whether proposal passed or not  Encoder A device that codes (converts) the data in one format to another. Encoding is done for variety of purposes in practical applications. E.g., Security, Efficiency, Speed, Minimal Design 2 Main types are, 1. Binary Encoder 2. Priority Encoder Binary Encoder An encoder is a combinational circuit that converts binary information in the form of a 2n input lines into N output lines Inputs Outputs Limitation - Only one input can be active at any given time. It would produce an error if more than one input are active at the same time. Binary Encoder: 4 x2Encoder  Binary Encoder: 4 x2Encoder Boolean Expression for, Q: Givea try : 8 x3Encoder Binary Encoder: 8 x3Encoder Binary Encoder: 8 x3Encoder Priority Encoders If more than one input is active high, then the binary encoder produces an output, which may not be the correct code. The Priority Encoder solves the problems mentioned above by allocating a priority level to each input. In priority encoders, more than one input can be high at any given time. Output corresponds to the currently active input which has the highest priority. So, when an input with a higher priority is present, all other inputs with a lower priority will be ignored  4 x 2 Priority Encoders Here, the input, Y3 has the highest priority, whereas the input, Y0 has the lowest priority. In this case, even if more than one input is ‘1’ at the same time, the output will be the binary code corresponding to the input, which is having higher priority.  4 x 2 Priority Encoders Here, the input, Y3 has the highest priority, whereas the input, Y0 has the lowest priority. In this case, even if more than one input is ‘1’ at the same time, the output will be the binary code corresponding to the input, which is having higher priority.  8 X 3 Priority Encoders D7 has the highest priority, whereas the input, D0 has the lowest priority.  Decoder Once the information is encoded (at the transmitting side) it must be decoded later (at the receiving side). Translate or decode coded information from one format into another An encoder is a combinational circuit that converts ‘n’ binary input signals into an equivalent code using 2n outputs. Decoder Sender Receiver 2x4Decoder 8 x3Decoder 8 x3Decoder Thanks! Do you have any questions?