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Explore the basics of half adders, full adders, decoders, multiplexers, and programmable logic devices in computer science with practical examples and applications. Learn how these circuits are implemented and their role in modern systems.
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CS 3501 - Chapter 3 (3A and 10.2.2) Dr. Clincy Professor of CS Dr. Clincy Lecture Slide 1
Half Adder - Combinational Circuits • Combinational logic circuits give us many useful devices. • One of the simplest is the half adder, which finds the sum of two bits. • We can gain some insight as to the construction of a half adder by looking at its truth table, shown at the right. Lecture
Full Adder - Combinational Circuits • We can change our half adder into to a full adder by including gates for processing the carry bit. • The truth table for a full adder is shown at the right. Lecture
Adders - Combinational Circuits • Just as we combined half adders to make a full adder, full adders can be connected in series. • The carry bit “ripples” from one adder to the next; hence, this configuration is called a ripple-carryadder. Today’s systems employ more efficient adders. Lecture
Decoder - Combinational Circuits • Among other things, they are useful in selecting a memory location according to a binary value placed on the address lines of a memory bus. • This is what a 2-to-4 decoder looks like on the inside. If x = 0 and y = 1, which output line is enabled? Output - Decoded message Input - Encoded message Lecture
Decoder – another example Lecture
Multiplexer - Combinational Circuits • A multiplexer does just the opposite of a decoder. • It selects a single output from several inputs. • This is what a 4-to-1 multiplexer looks like on the inside. Depending the “select input” combination, 1 of 4 data inputs is chosen for output If S0 = 1 and S1 = 0, which input is transferred to the output? Lecture
Multiplexer - Combinational Circuits Can also use multiplexers to implement logic functions Given this truth table, group X1,X2 being 00, 01, 10 and 11 – notice what happens with X3 • 3-input truth table can be done with a 4-input mux • 4-input truth table can be done with a 8-input mux • 5-input truth table can be done with a 16-input mux • Etc.. Also explain how the Mux is used to implement data comm’s FDM and TDM Lecture
10.2.2 - Programmable Logic Devices (PLD) All possible combinations of inputs ANDed ••• All possible combinations of ANDed inputs ORed Re-explain Sums of Products and relationship to PLDs Lecture
10.2.2 - Programmable Logic Array (PLA) Ability to program a PLD, is called a PLA Lecture
10.2.2 - Programmable Array Logic (PAL) For a PLA, both the AND array and OR array are programmable For a PAL, the AND array is programmable and the OR array is fixed Lecture
10.2.2 - Complex Programmable Logic Devices (CPLDs) CPLDs are comprised of 2 or more PALs Lecture
10.2.2 - Field Programmable Gate Arrays (FPGAs) PAL chips are somewhat limited in size due to the fact they have output pins for each sum-of-product circuit FPGA overcome this size limitation by using a general interconnection. General interconnection PAL Lecture