Title: Counting in 1s and 0s and Logic Gates
1 Counting in 1s and 0s and Logic Gates
- GEMS Seminar 1
- April 7, 2005
- Presenter Ana Maria
2Topics of Discussion
- Learning how to count in 1s and 0s
- Writing Our Names in 1s and 0s using ASCII
- What is an AND, NAND, OR, NOR Gates
- Further Applications
- Questions and Answers
3Logic Circuits
- So what Reads these 1s and 0s?
- Logic Gates starting from the fundamental Gates
of AND, OR, NOT.and so forth. Having a series of
combinations of these create latches and bigger
systems.
4Majors Using this Knowledge
- Computer Engineering Combine aspects of Computer
Science and Electrical Engineering, creates the
bridge between the software and hardware. - Electrical Engineering, deal with the hardware,
responsible for the little components inside a
computer - Computer Science, are programmers who deal with
the softwaretell computers what to do.
5Websites to Visit
- Animation of AND and OR Gates
- www.acad.humberc.on.ca/ ceng103/logic2.html
- Using AND and OR Gates to Turn on Lights
- www.technologystudent.com/ elec1/dig2.htm
6What Base do we count in?
- We count in base 10.
- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- 11-Notice how the 1 in the 10ths place will not
increment until it reaches 10 once more) 12, 13,
14, 15, 16, 17, 18, 19 - 20( it Changed!!!)
7What base do computers count in?
- Computers count with 1, 0s that is called binary
(bin-meaning 2). AMAZING! - Computers transmit data in strings of 1s and 0s
called bits - We only use the numbers 1, 0 with a base of 2.
8What is Base 2?
- Binary has a base 2, the only number that changes
is the exponent - Baseexponent 201n.
- 20 1 , 21 2,
- 22 2x2 4, 23 2x2x2 8
-
9Creating the Number 9
- How do you create the number 9 in Binary?
- 81 9, 54 9
- 72 9, etc.
- The one we can represent is 8 1 9
- Given 4 places.
- ___ ___ ___ ___
- 8 4 2 1
- 8 0 0 1
- 1 0 0 1
-
10Closer Look into Binary
11Lets try some Problems
- What is the number 8 in binary?
- What is the number 5 in binary
- What is the highest number using 4 digits?
12Lets try some Problems
- What is the number 8 in binary?
- _ _ _ _
- 8 4 2 1
- In Binary 1000
- What is the number 5 in binary
- _ _ _ _
- 8 4 2 1
- In Binary 0101
- What is the highest number using 4 digits?
- _ _ _ _
- 8 4 2 1
- In Binary 1111 In base 10 15
13Activity
- Write your neighbors first name or their nick
name in binary using the ASCII Table - Ana 0100001 01101110 0110001
- Hana 01001000 0100001 01101110
0110001 - Bev 01000010 01100101
14The TRUTH about AND
- We analyze gates in terms of truth tables
- Multiplying (x, , /\)
- is the same as ANDING the result is AB
- We Use variables like A, B as the inputs
- AND Gates require both to be 1
Truth Table INPUTS OUTPUTS
15The Truth About OR GATES
Truth Table INPUTS OUTPUTS
- An OR gate will be on if, at least one of them is
High that is 1. - We used the symbol ( , \/ ) to indicate an or
operation.
16NOT, INVERTER
- The Inverter Gives the exact opposite of what is
put in. - You Put a Low (0) it will give you a High (1)
- The Sign of inverting is an apostrophe or a bar
- A
- or _
- A
Truth Table INPUTS OUTPUTS
Inverter
17So, What happens when you NOT an AND?
- You will get a NAND GATE!!!
- Your result will have all the original AND
outputs Inverted.
18Truth Table and NAND Diagram
19SoWhat about an Inverted OR?
- Try it yourself
- What do you think its called?
- GOOD JOB!!
20Truth Table of Inverted OR
- What do you think its called?
- A NOR
- GOOD JOB!!
21Truth Table and OR Diagram
22FUN WITH GATES
- Line Up in Groups of 4
- 2 People are the INPUTS
- 1 Person is the OUTPUT
- 1 Person is the INVERTER
23Rules of the GAME
- There are two Lines
- Duck to represent low (0)
- Stand tall to represent High(1)
- The Inverter person has to tap the other people
to put them in the correct position. - Make the following configurations of Gates!
24MAKING AND and OR Gates
- MAKE the Truth Table of the AND Gate
- Try Inputs 00, 01, 10, 11
- Make the Truth Table of the OR gate
- How about the NAND and the NOR?
25Questions?
- I might be able to answer some questions, but
write them down and Ill get the answer for you
by next seminar! - ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
26THANKS For Your Attention!!
- We will be taking a 10min break then talk to
someone over the AG.. - Be back in 10 Please! ?
-