CS101 Lecture 05: Logic Gates and Binary Addition
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1 CS101 Lecture 05: Logic Gates and Binary Addition Logic Gates Binary Number Addition Some images copyright Jones and Bartlett Thanks to Charles Petzold for some diagrams and ideas Aaron Stevens 28 January 2013 What You ll Learn Today Review: How do we add in binary? Some fundamentals of electric circuitry Using electric circuits to implement logic What is the relationship between binary numbers and electronic computation? Why should you care? This is what a computer actually does! 2 1
2 Binary: Add with Carry Remember that there are only 2 digits in binary, 0 and is 0 with a carry of 1 Operands! 1 1 0!! !! !! ! Carry Values Sum Hint: work right to left An 8-bit Adder Consider this 8-bit adder: Notice how the carry out from one bit s adder becomes the carry-in to the next adder
3 A binary Adding Machine Anatomy of a Flashlight A flashlight has 3 main components: A battery A bulb A conductor (e.g. wire) 6 3
4 Anatomy of a Flashlight Here the wires are connected, which forms a sort of circle, called a circuit. The circuit allows electrons to move from a source to a sink. Along the way, the bulb is lit. 7 Edison s First Rule of Electricity You cannot make electricity flow without a plug. or, more precisely: Electric current flows through a closed circuit. If the wire is not connected, the circuit is said to be open, and the electrons don t flow.* *of course, electrons can flow through the air (e.g. lightning, arcs, etc.) but let s keep it simple for now 8 4
5 Light Switch Circuits We will now consider several examples to demonstrate some techniques for wiring circuits with light switches. This link brings up a great animated/interactive version, but I ve reproduced still pictures on the following slides Switches in Series Consider this arrangement, called wiring in series. (the light is off) 10 5
6 Switches in Series Now we close one switch (e.g. connect the wire) (the light is still off) 11 Switches in Series Now we close the other switch (e.g. connect the wire) (the light is still off) 12 6
7 Switches in Series Now we close both switches (e.g. connect the wire) (now the light is on) 13 Switches in Series: Summary Left Switch Right Switch Light Bulb OFF OFF OFF OFF ON OFF ON OFF OFF ON ON ON Light is on if and only if both switches were closed (on). 14 7
8 Building Blocks These wiring arrangements are the fundamental building blocks of computer circuitry. Each switch has 2 states (on or off) Each light bulb has 2 states (on or off) We can abstractly describe switches and bulbs as each having a 1 bit state. 15 Building Blocks Gates (not Bill) Simple electric circuits which perform like our light switch examples. The input values explicitly determine the output values. We assume the switch is controlled by a electronic input rather than a physical switch. 16 8
9 Describing Gates and Circuits We describe gates and circuits using: Logic diagrams A graphical representation of a circuit; each gate has its own symbol. Truth tables A table showing all possible input value and the associated output values. 17 AND Gate The AND gate accepts two input signals. The output is 1 if and only if both inputs are 1. Otherwise the output is 0. Just like wiring in series. 18 9
10 Switches in Parallel Now let s try connecting the switches a little differently. Consider this arrangement, called wiring in parallel. (the light is off) 19 Switches in Parallel Now we close just the top switch. (the light came on!) 20 10
11 Switches in Parallel Or we just the bottom switch. (the light is still on!) 21 Switches in Parallel Or we close both switches! (the light is still on!) 22 11
12 Switches in Parallel: Summary Top Switch Bottom Switch Light Bulb OFF OFF OFF OFF ON ON ON OFF ON ON ON ON Light is on if either switch alone, or both switches together are closed (on). 23 OR Gate The OR gate accepts two input signals. The output is 1 if either input is 1. The output is 0 if both inputs are 0. Just like wiring in parallel
13 A 3-Way Switch Consider this arrangement, called wiring a 3-way switch. Both switches are to the left (the light is off). 25 A 3-Way Switch Now we have one switch left, one switch right. (the light is on)
14 A 3-Way Switch Now we have one switch right, one switch left. (the light came one) 27 A 3-Way Switch Now we have both switches to the right. (now the light is off again) 28 14
15 3 Way Switch: Summary Left Switch Right Switch Light Bulb LEFT LEFT OFF LEFT RIGHT ON RIGHT LEFT ON RIGHT RIGHT OFF Light is on if and only if one switch is left and the other switch is right 29 XOR Gate An XOR gate accepts two input signals. When the 2 inputs differ, the output is 1 When both inputs are the same, the output is 0 Just like wiring with a 3-way switch
16 Summary: Logic Gates Recall: gates control the flow of electric current. AND Gate (wiring in series) Output is on if BOTH inputs are on OR Gate (wiring in parallel) Output is on if EITHER input is on XOR Gate (3-way switch) Output is on if switches DIFFER from each other Output is off if switches are SAME as each other 31 What You Learned Today = Circuits Basic logic gates (AND, OR, XOR) 32 16
17 Announcements And To Do Readings: Reed chapter 7, pp Wikipedia: (introductory remarks about gates on integrated circuits) HW02 due Wednesday 1/30 Quiz 1 on Friday 2/1 Covers material from lectures 1-4 (i.e., not including today) 33 17
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