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4-bit Adder, Multiplexer, Timing Diagrams, Propagation Delays

This lecture covers the concept of a 4-bit adder, multiplexers, timing diagrams, and propagation delays in circuits. It explains gate delay, Quartus II timing simulation, 4-bit ripple carry adders, critical paths, and multiplexers. It also includes exercises on subtractors.

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4-bit Adder, Multiplexer, Timing Diagrams, Propagation Delays

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  1. CSE 140L Lecture 3 4-bit adder, multiplexer, timing diagrams, propagation delays CK Cheng

  2. Timing behavior • Real circuits have delays • Gate delay – time for an output of the gate to change after its input changes • We can simulate timing delays in Quartus II to see these delays

  3. Gate delay • Notice rise time, fall time, and gate delay: input output input output

  4. Quartus II Timing Simulation Notice the glitches and delay in the output

  5. 4-bit Ripple Carry Adders • Chain 4 1-bit full adders together. Connect the carry-out of the previous adder and the carry-in of the next adder. • Worst delay path (critical path): from A0, B0, or C0 to S3, or C4

  6. Critical Path for worst delay Propagation from C0 to C4 • C4 changes as C0 toggles C0 1110 0001 C4

  7. Multiplexers -Multiplexers (MUXes) are like selectors. There is one output, 2 or more inputs, and a “selector” input that determines which of those inputs gets outputed. -Allows several devices to share one single line. This is a 2:1 mux. It has 2 inputs, 1 output. Because there are only 2 inputs, S is one bit. If S=0, then we output A. If S=1, then we output B. A MUX Z B S

  8. Multiplexers -The truth table for the 1-bit 2:1 MUX. When S=0, the MUX will select A as its output. It doesn’t matter what B is. Likewise, When S=1, B is selected as output. The boolean equation: Z = AS’ + BS

  9. Multiplexers -If S is 0, then I0 will pass and I1 is blocked. Thus, y=I0. -Likewise, if S is 1, y=I1.

  10. Multiplexers -We can also make a 4:1 MUX using three 2:1 MUX If S1S0 = 00, then S1 will select MUX from A and B. Since S0=0, Z= A. A 0 MUX 1 B 0 Z MUX S0 Z 1 C 0 MUX S1 D 1

  11. Multiplexers -We can make 4:1 and above MUXes too. -With 4 inputs, our selector needs to have two bits.

  12. Exercises Subtractors: a. Subtraction b. One’s Complement c. Two’s Complement

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