Lecture 05 - Combinational Logic¶
- Chapter 2 in [harris2012digital]
- Chapter 4 until 4.3 and 4.5 in [harris2012digital]
- Chapter 3 until 3.3 in [patt2005introduction]
02:00 Video assignment: Onur Mutlu - Future Computing Architectures - ETH Zurich Inaugural Lecture (May 15, 2017)
04:00 Bloom filter recall, it was mentioned there.
14:00 Bloom filter advantages and disadvantages. Bloom filters are also used by search engines.
16:45 Bloom filters never overflow unlike fixed-size tables. You can insert new elements without increasing storage space. However this will increase false positive rate likely. It is scalable.
20:00 Takeaways: This field has probably many challenging and exciting problems that no one has attacked. It is driven by huge hunger for data and its analysis (“Big data”). We can easily collect more data than we can analyze/understand. Field is driven by significant difficulties. Three walls: energy, reliability, complexity.
22:30 Dream and they will come.
24:00 A memory access consumes ~1000x the energy of a complex addition. Communication Dominates Arithmetic (Daily, HiPEAC 2015).
35:30 Three key components of a computer: computation, communication and storage (memory).
39:45 Differences between microprocessors, FPGAs, ASICs.
42:30 Introduction to transistors. Today processors have transistors at billion scale.
43:40 MOS Transistor: Conductors (Metal), Insulators (Oxide) Semiconductors. It is controlled switch. N and P types are mentioned.
51:00 Logic gates.
51:34 CMOS technology = nMOS + pMOS. C stands for complementary.
52:50 Gender neutrality in Turkish :). “Haklısınız hocam :)”
54:00 Operation of a simple CMOS inverter.
1:00:11 CMOS NAND gate.
1:05:30 NAND gate is “logically complete”. You can build any logic just only using NAND gates.
Note that AND gate doesn’t have this property. You can’t invert using AND. NAND and NOR are functionally complete.
1:06:00 CMOS AND gate. AND gate is more complicated than NAND in terms of number of transistors.
1:07:00 General CMOS structure has PMOS transistors connected to VCC and the output. It works as pull-up network. NMOS transistors are connected to GND and form a pull-down network.
1:08:40 Common logic gates.
1:10:45 Moore’s Law is mentioned.
1:13:44 Dennard scaling is mentioned.
1:15:00 What is the limit on transistor size? We don’t know!
1:15:45 Heat is a real problem in computer design.
1:18:15 Combinational logic is memoryless. It doesn’t remember anything. Some books call Combinatorial Logic. Sequential Logic has memory.
1:19:00 functional specification and examples. First example: full 1-bit adder.
1:21:50 Simple equations: NOT / AND / OR.
1:22:20 [boole1847mathematical] is mentioned.
1:23:07 Axioms of Boolean Algebra
1:24:45 Duality in Boolean Algebra. All the axioms come in dual form. This form can be derived by replacing: every AND with OR, every OR with AND, every 1 to 0, every 0 to 1 BUT don’t change any literals or play with complements.
1:25:50 Some useful Boolean Algebra laws.
- Dennard scaling
- From Wikipedia: “Originally formulated for MOSFETs, it states, roughly, that as transistors get smaller, their power density stays constant, so that the power use stays in proportion with area; both voltage and current scale (downward) with length” and “Therefore, in every technology generation the transistor density doubles, the circuit becomes 40% faster, and power consumption (with twice the number of transistors) stays the same.” See: [dennard1974design]
- functional specification
- Describes relationship between inputs and outputs
- Moore’s Law
- See: [moore1965cramming] Moore is one of founders of Intel. He says that component on a chip counts double every other year. Some says that interval is 18 months. Key idea is a fixed interval. Size of transistor is shrinking so we can put more on a chip. Also cost of per circuit varies. We can say that rule was still valid until 2016. (I don’t mean that this is invalid since 2016. That was the data shown given on the slides)
- timing specification
- Describes the delay between inputs changing and outputs responding
Section author: Alper Yazar