1 / 14

ECE 3110: Introduction to Digital Systems

ECE 3110: Introduction to Digital Systems. Combinational-Circuit Synthesis. Previous…. Circuit Analysis. Combinational circuit synthesis. Description--->combinational logic circuit. Description: Word description of a problem using English-language connectives

yachi
Download Presentation

ECE 3110: Introduction to Digital Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ECE 3110: Introduction to Digital Systems Combinational-Circuit Synthesis

  2. Previous… • Circuit Analysis

  3. Combinational circuit synthesis • Description--->combinational logic circuit. • Description: • Word description of a problem using English-language connectives • Write corresponding logic expression/truth table • Manipulate the expression if necessary. • Build a circuit from the expression. • A circuit realizes an expression if its output function equals that expression, and the circuit is called a realization of the function.

  4. Prime-number detector Word description: Given a 4-bit input combination N= N3N2N1N0, This function produces a 1 output for N=1,2,3,5,7,11,13, and produces a 0 otherwise.

  5. Brute-force design row N3 N2 N1 N0 F 0 0 0 0 0 0 1 0 0 0 1 1 2 0 0 1 0 1 3 0 0 1 1 1 4 0 1 0 0 0 5 0 1 0 1 1 6 0 1 1 0 0 7 0 1 1 1 1 8 1 0 0 0 0 9 1 0 0 1 0 10 1 0 1 0 0 11 0 0 1 1 1 12 1 1 0 0 0 13 1 1 0 1 1 14 1 1 1 0 0 15 1 1 1 1 0 • Truth table --> canonical sum (sum of minterms)

  6. Minterm list --> canonical sum

  7. Combinational-Circuit Design • Sometimes you can write an equation or equations directly using “logic” (the kind in your brain). • Another example: Alarm

  8. Description: The ALARM output is 1 if the PANIC input is 1, or if the ENABLE input is 1, the EXITING input is 0, and the house is not secure; the house is secure if the WINDOW,DOOR, and GARAGE inputs are all 1. Algebraic expression Corresponding Circuit

  9. Alarm-circuit transformation • Sum-of-products form • Useful for programmable logic devices • “Multiply out”:

  10. Circuit manipulation • Standard gate types • AND, OR, Inverter, NAND,NOR • In most logic technologies, inverting gates like NAND/NOR are faster than non-inverting gates like AND/OR • Translate any logic expression into an equivalent sum-of-products expression by multiplying it out. • Translate any logic expression into an equivalent sum-of-products expression by adding it out.

  11. AND-OR NAND-NAND Sum-of-products form

  12. Any sum-of-products expression can be realized in either as an AND-OR circuit or as a NAND-NAND circuit. • Dual statement is also true: Any product-of-sums expression can be realized in either as an OR-AND circuit or as a NOR-NOR circuit.

  13. OR-AND NOR-NOR Product-of-sums form P-of-S preferred in CMOS, TTL (NAND-NAND)

  14. Next… • Minimization using Karnaugh maps

More Related