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Combinational logic circuits. How ALU & associated components are built using Half Adder, Full Adder, Ripple carry adder, Decoders, & Multiplexer

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- 1. Combinational Circuits CS2052 Computer Architecture Computer Science & Engineering University of Moratuwa Dilum Bandara Dilum.Bandara@uom.lk
- 2. Blocks of a Microprocessor 2 Literal Address Operation Program Memory Instruction Register STACK Program Counter Instruction Decoder Timing, Control and Register selection Accumulator RAM & Data Registers ALU IO IO FLAG & Special Function Registers Clock Reset Interrupts Program Execution Section Register Processing Section Set up Set up Modify Address Internal data bus Source: Makis Malliris & Sabir Ghauri, UWE
- 3. Combinational Circuits Binary values of outputs are a function of binary combination of inputs Outputs at any given time are entirely dependent on inputs that are present at that time 3 Combinational Circuits n inputs m outputs
- 4. Adding 2 Numbers Write the truth table for addition of 2 bits A & B Write Boolean representation for Sum & Carry S = A/B + AB/ = A B C = AB 4 A B Sum (S) Carry (C) 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1
- 5. Adding 2 Numbers (Cont.) Draw logic circuit This is called a half adder 5 Source: Wikipedia.org
- 6. Adding 2 Numbers & a Carry Write the truth table for addition of 2 bits A & B as well as a carry from previous low-order bit 6 A B Cin S Cout 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1
- 7. Adding 2 Numbers & a Carry (Cont.) Write Boolean representation for Sum & Carry Hint – use k-maps S = (A B) Cin Cout = AB + (A B)Cin 7 ab c 00 01 11 10 0 1 1 0 1 0 0 1 0 1 ab c 00 01 11 10 0 1 0 1 1 1 0 0 1 0 S = Cout =
- 8. Adding 2 Numbers & a Carry (Cont.) Draw logic circuit This is called a full adder 8 Source: www.setupsolution.com/how-to-design-a-half-adder-and-full-adder-in-verilog-at-gate-level-modeling/
- 9. Schematic Representation of Full Adder 9 Source: http://en.wikibooks.org (A B) AB
- 10. n-bit Adder (Ripple Carry Adder) 10
- 11. Decoders Suppose a simple microprocessor supports following 2 instructions ADD LOAD When these instructions execute they’ll need to activate different circuits Which circuit is determined by 2 most significant bits 11
- 12. Decoders Converts binary data from n coded inputs to a maximum of 2n unique outputs Called n-to-2n decoder 12 Decoder b0 b1 Adder Loader d0 d1 d2 d3
- 13. Decoders Truth table for a 2-to-4 decoder 13 b0 b1 d0 d1 d2 d3 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1
- 14. Decoders Draw logic circuit of a 2-to-4 decoder 14 b0 b1 d0 d1 d2 d3 Source: www.allaboutcircuits.com/vol_4/chpt_9/4.html
- 16. Decoder Expansion Build a 3-to-8 decoder using 2-to-4 decoders 16 Source: http://dc167.4shared.com/doc/ or00nekd/preview.html Source: www.teachurselfece.com/2012/ 02/decoders.html
- 17. Decoders (Cont.) ADD LOAD Also helps us select which registers to use 17
- 18. 18 Use of Decoders Inside CPU A E D C B ALU AddressBus Control Unit IR FLAG ALU PC +1 DataBusCTRLBus
- 19. Encoders Reverse process of a decoder 4-to-2 encoder 3-to-8 encoder 19 Source: www.electronics-tutorials.ws/combination/comb_4.html
- 20. Encoders Draw logic circuit of a 4-to-2 encoder 20 D0 D3 D1 D2 Q0 Q1
- 23. Internal Structure (Cont.) 23 Source: www.transtutors.com/homework-help/computer- science/computer-architecture/cpu/general-register-organization/
- 24. Multiplexer Receives binary data from 2n lines & connect them to a single output line based on a selection By applying a control signals we can steer any input to the output 24 Multipl- exer d0 d1 s0 s1 q d2 d3
- 25. Multiplexer (Cont.) Truth table 25 s0 s1 q 0 0 d0 0 1 d1 1 0 d2 1 1 d3
- 26. Multiplexer (Cont.) Logic circuit 26 d0 d1 d2 d3 q Source: www.ee.surrey.ac.uk/Projects/CAL/digital-logic/multiplexer/index.html
- 27. 8-to-1 Multiplexer 27 Source: http://users.cis.fiu.edu/~prabakar/cda4101/Common/notes/lecture08.html
- 28. 8-to-1 Multiplexer using 4-to-1 & 2-to-1 Multiplexers 28 Source: www.exploreroots.com/dc28.html
- 29. Demultiplexer Reverse process of a multiplexer By applying a control signals we can steer the input signal to one of the output lines 29 Demult- iplexer q0 q1 s0 s1 d q2 q3
- 30. Demultiplexer (Cont.) Truth table Logic circuit 30 s0 s1 q0 q1 q2 q3 0 0 d 0 1 d 1 0 d 1 1 d d q0 q1 q2 q3 s0 s1Source: http://do-area.blogspot.com/p/multiplexer-demultiplexer.html
- 31. Demultiplexer Using Decoder 31 Source: http://en.wikipedia.org
- 32. Multiplexer/Demultiplexer - Application in Telecommunication 32Source: http://digilogwiki.com/index.php?title=Multiplexers/Demultiplexers