数字电路 讲义 353f13sept20-slides-3x3

AB =
1 if both A and B are 1 0 otherwise
Let’s write the truth table for AND.
ENEL 353 F13 Section 02 Slides for Lecture 6
ENEL 353 F13 Section 02 Slides for Lecture 6
slide 10/21 ENEL 353 F13 Section 02 Slides for Lecture 6
slide 11/21 ENEL 353 F13 Section 02 Slides for Lecture 6
This version uses unsigned binary encoding for positions 0 to 15. Why is this encoding a poor design choice?
If the light and dark markings on the spinning disk are organized using a Gray code, that eliminates the problem of having two or more bits change at almost but not exactly the same time.
ranges for two’s-complement systems overflow in two’s-complement addition BCD (binary coded decimal) codes for decimal digits Gray codes
A little more about Gray codes. Introduction to logic gates.
20 September, 2013
ENEL 353 F13 Section 02 Slides for Lecture 6
Previous Lecture
slide 2/21 ENEL 353 F13 Section 02 Slides for Lecture 6
Today’s Lecture
slide 3/21
The AND gate
Here is the symbol and the algebraic notation: A Y = AB B
One way to remember the symbol is to remember that the word AND contains a D, and the symbol looks like a D. An alternate algebraic notation for AND uses the · symbol, as in Y = A · B. Here is how the AND operation is defined:
slide 15/21
Truth tables
A truth table describes a combinational logic element by making a list of the values of the output for all possible combinations of input bits. (We’ve already seen the truth table for the 1-bit full adder.) Let’s write out the very simple truth tables for a NOT gate and a buffer.
A 4-bit shaft encoder: Optical sensors make a digital measurement of the rotation angle of a spinning metal disk. This could be used for a digital weathervane, indicating one of 16 wind directions N, NNE, NE, ENE, . . . , NNW.
A logic gate is a combinational logic circuit that has one or more inputs, each of which is a bit; exactly one output, which is a bit.
According to this definition, is the full adder a logic gate?
sliபைடு நூலகம்e 12/21
Graphical and algebraic notations for some common 1- and 2-input logic gates
A
Y =A
A
B
A
Y =A
A
A
B
B
Y = AB
A
A
B
B
Y =A+B
A
B
Y =A⊕B Y = AB Y =A+B Y =A⊕B
We’ll now examine these gates one or two at a time . . .
Very precise shaft encoders can measure very small changes in angles in industrial equipment. For example, a 12-bit shaft encoder measures rotation angle to within 360◦/212 = 0.088◦.
ENEL 353 F13 Section 02 Slides for Lecture 6
Combinational versus Sequential Logic
slide 7/21 ENEL 353 F13 Section 02 Slides for Lecture 6
slide 8/21 ENEL 353 F13 Section 02 Slides for Lecture 6
Slides for Lecture 6
ENEL 353: Digital Circuits — Fall 2013 Term
Steve Norman, PhD, PEng
Electrical & Computer Engineering Schulich School of Engineering University of Calgary
The outputs of a sequential logic circuit depend on the history of its input values.
A B Cin
full adder
Cout S
The values of Cout and S depend on what the values of A, B, and Cin are RIGHT NOW, not what they were a few minutes ago, or even a few nanoseconds ago.
ENEL 353 F13 Section 02 Slides for Lecture 6
Practical shaft encoders use Gray codes
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extra 0 not part of either code
n-bit Gray code
...
0
...
n-bit binary code
1-input gates
A NOT gate, also called an inverter:
A
Y =A
In A is the input and Y is the output. The “bubble” in the symbol indicates inversion: 0 converted to 1, and 1 converted to 0. The equation Y = A is read, “Y equals NOT A.”
Example combinational circuit: 1-bit full adder
What does the term logic gate mean?
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It’s IMPORTANT to know what these words mean.
The outputs of a combinational logic circuit depend only the current values of its inputs.
An alternate notation for the NOT operation
The “overline” is probably the most common notation for the NOT operation, but there is another symbol in wide use. Many textbooks and other documents use the symbol (“prime”) instead. This includes the textbook used last year in ENEL 353. This year we will use an “overline” for the NOT operation, to be consistent with this year’s textbook. If you see A in course material from past years, translate that in your head to A.