Chapter 3: Combinational Logic Design Flashcards
What is an universal logic gate?
A gate type that alone can be used to implement all possible Boolean functions (it is said to be functionally complete)
What gates are universal gates?
The NAND and NOR gates
How can you obtain a NOT gate from a NAND gate?
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How can you obtain an AND gate from two NAND gates?
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How can you obtain an OR gate from three NAND gates?
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What are the three steps to implement a given digital circuit with only NAND gates?
1) Replace each AND gate and OR gate with its equivalent circuit using NAND gates and NOT gates
2) Cancel all inverter pairs
3) Replace each inverter with its equivalent NAND gate
What is decoding?
The conversion of an n-bit input code to an m-bit output code with n <= m <= 2^n
What is a decoder?
A decoder is a combinational circuit with an n-bit binary code applied to its inputs and an m-bit binary code appearing at the outputs
What is a 1-to-2-line decoder?
A combinational circuit that decodes the single input 0 to the two outputs 1,0 and the single input 1 to the two outputs 0,1
How can the function, n-to-m-line decoding with enabling, be implemented?
By attaching m enabling circuits to the AND gates leading to the decoder outputs
How can you use decoders to form a sum-of-minterms implementation?
By using a decoder to generate the minterms and combining them with an external OR gate to form the sum-of-minterms implementation
What is the truth table for a 1-bit binary adder?
X Y Z C S
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
What is an encoder?
A digital function that performs the inverse operation of a decoder
How many input lines and output lines does an encoder have?
2^n (or fewer) input lines and n output lines
What is a priority encoder?
A combinational circuit that implements a priority function, which means if two or more inputs are equal to 1 at the same time, the input having the highest priority takes precedence
What is a multiplexer (MUX)?
A combinational circuit that selects binary information from one of many input lines and directs the information to a single output line
How many select inputs does a 2-to-1-line multiplexer need?
Only 1
Given a 2-to-1-line multiplexer with input I0 and input I1. When is output Y = 1 when S = 0?
When S = 0 the output Y is exactly equivalent to the input I0. So, Y is 1 whenever I0 is 1.
Given a 2-to-1-line multiplexer with input I0 and input I1. When is output Y = 1 when S = 1?
When S = 1 the output Y is exactly equivalent to the input I1. So, Y is 1 whenever I1 is 1.
What is the circuit symbol for a multiplexer?
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A multiplexer is also called what?
Data selector
What kind and how many multiplexers do we need to implement a 1-bit binary adder with them?
We need two 8-to-1 multiplexers (implementation with two 4-to-1 multiplexers is also possible)
What is an arithmetic circuit?
A combinational circuit that performs arithmetic operations such as addition, subtraction, multiplication, and division with binary numbers
What is a half adder?
A combinational circuit that performs the addition of two bits
