1. CSCE 211: Digital Logic Design
Chin-Tser Huang
University of South Carolina

2. Chapter 5: Designing Combinational Systems

3. Iterative System
A system implemented with multiple copies of a smaller circuit
Consider 4-bit adder as an example
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4. Delay in Combinational Logic Circuits
When the input to a gate changes, the output of that gate will not change instantaneously
Instead, there is a small delay ∆
If the output of one gate is used as the input to another gate, the delays will accumulate
The output is stable after the longest delay path
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5. Delay in Combinational Logic Circuits
Hazard (or glitch)
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6. Example of Delay
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7. Cascading 4-bit Adders
Can cascade multiple 4-bit adders if larger adders are needed
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8. Binary Decoder
A binary decoder is a device that, when activated, selects one of several output lines, based on a coded input signal
The input is an n-bit binary number, and there are 2n output lines
Some decoders also have one or more enable inputs
Decoders are often used to select one of many devices
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9. Active High Decoder
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10. Active Low Decoder
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11. Decoder with Enable
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12. 74138 Decoder
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13. 74138 Decoder
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14. Use 4 3-to-8 Decoders
to Select from 32 Devices
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15. Use Decoder to Enable Another Decoder
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16. Multiplexers
A multiplexer is a switch that passes one of its data inputs through to the output, as a function of a set of select inputs
Sets of multiplexers are often used to choose among several multibit input numbers
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17. Two-way Multiplexer
out = w if S = 0;
out = x if S = 1
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18. Four-way Multiplexer
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20. Three-variable Function Implemented with Multiplexer
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21. Gate Arrays
Also known as programmable logic device (PLD) or field programmable gate array (FPGA)
An efficient way of implementing complicated systems
Can implement SOP expressions which are sums of some common product terms
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22. Structure of a Gate Array
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23. An Example of Gate Array
f = a’b’ + abc
g = a’b’c’ + ab + bc
h = a’b’ + c
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24. Three Types of Combinational Logic Arrays
Programmable Logic Array (PLA)
User specifies all of the connections in both the AND array and the OR array
Read-Only Memory (ROM)
The AND array is fixed – like a decoder consisting of 2n AND gates for n inputs
User specifies the connections in the OR array
Programmable Array Logic (PAL)
The connections to the OR gates are specified; user determines the AND gate inputs
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25. Design with Read-Only Memories
Only need a list of minterms for
each function. For example,
W(A, B, C, D) = ∑m(3, 7, 8, 9, 11, 15)
X(A, B, C, D) = ∑m(3, 4, 5, 7, 10, 14, 15)
Y(A, B, C, D) = ∑m(1, 5, 7, 11, 15)
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26. Structure of a PAL
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