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# Combinational Circuits & Sequential Circuits

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### Combinational Circuits & Sequential Circuits

1. 1. Combinational Circuits & Sequential Circuits By:-Gourav Kottawar 3/11/2016
2. 2. Contents 3.1 Half / Full Adder 3.2 Decoder / Encoder 3.3 Multiplexer / Demultiplexer, 3.4 Flip Flops - SR, D, JK, Master – Slave, Edge Triggered D flipflop with timing diagram 3.5 Shift Registers (Any one type) 3.6 Introduction to Counters, Synchronous & Asynchronous counter, Binary counter, mod-10 Counter 3/11/2016 By:-Gourav Kottawar
3. 3. Introduction  There are two types of logic circuits  Combinational Circuits  Formed by combination of different logic circuits  Outputs depend on the current inputs  Ex- Multiplexer, De multiplexer, Encoder, Decoder  No memory allocation required  Sequential Circuits  Outputs depend on current and previous inputs  Requires separating previous, current and future  Called states or tokens  Example: Finite State Machines (FSMs), Pipelines 3/11/2016 By:-Gourav Kottawar
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5. 5. Difference between Combinational and sequential circuits Combinational Sequential Output of any instance of time depends only upon the input variables Output is generated dependent upon the present input variables and also on the basis of past history of these inputs Memory unit is not required. i.e. it doesn’t allocate any memory to the elements. Memory unit is required. . i.e. it allocates any memory to the elements. Faster Slower Easy to design Difficult Parallel adder Serial adder Ex- Half and full adder Half and full subtractor MUX , DEMUX Ex- Flip flops Shift registers Binary counters 3/11/2016 By:-Gourav Kottawar
6. 6. Adders  Computers implement arithmetic computations such as addition, subtraction, multiplication, division and many such operations using the concept of combinational circuits.  Ex- 1 1 0 0 1 1 1 0 0 1  When addition of two k bits is computed the answer must be of k bits.  But If the numbers are unsigned binary , the result can be K+1 bits.  This k+1 bit is carry.  Three types of Adder 1. Half Addder 2.Full Adder 3.Ripple carry Adder 3/11/2016 By:-Gourav Kottawar
7. 7. 1. Half Adder 3/11/2016 By:-Gourav Kottawar
8. 8. 1. Half Adder  The implementation of half adder using  The implementation of half adder using exclusive–OR and an AND gates is used to show that two half adders can be used to construct a full adder.  The inputs to the XOR gate are also the inputs to the AND gate. 3/11/2016 By:-Gourav Kottawar
9. 9. Half Adder  Draw backs 1. Doesn’t handle carries 2. Doesnot do further processing on carries. 3/11/2016 By:-Gourav Kottawar
10. 10. 2. Full Adder  Full Adder is a combinational circuit that performs the addition of three bits (two significant bits and previous carry).  It consists of three inputs and two outputs, two inputs are the bits to be added, the third input represents the carry form the previous position.  The full adder is usually a component in a cascade of adders, which add 8, 16 etc binary numbers. 3/11/2016 By:-Gourav Kottawar
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16. 16. 3. Binary Adder (Asynchronous Ripple-Carry Adder)  A binary adder is a digital circuit that produces the arithmetic sum of two binary numbers.  A binary adder can be constructed with full adders connected in cascade with the output carry form each full adder connected to the input carry of the next full adder in the chain.  The four-bit adder is a typical example of a standard component. It can be used in many application involving arithmetic operations. 3/11/2016 By:-Gourav Kottawar
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18. 18. Example 3/11/2016 By:-Gourav Kottawar
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