PHY 201 (Blum)1 Transistor Odds and Ends

PHY 201 (Blum)2 RTL NOR

PHY 201 (Blum)3 NOT from NOR

PHY 201 (Blum)4 OR from NOR

PHY 201 (Blum)5 AND from NOR

PHY 201 (Blum)6 Other Logic Families As one has an increasing number of logic gates one has to be concerned with their power performance and stability. The logic gates can be made out of various combinations of resistors, diodes, and transistors. They differ in power and stability. Let us examine an inverter from the TTL (transistor- transistor logic) family.

PHY 201 (Blum)7 TTL Inverter

PHY 201 (Blum)8 TTL Inverter

PHY 201 (Blum)9 On-Off Recall that a transistor can be thought of a switch. – When the switch is off, the transistor has very high resistance. – When the switch is on, the transistor has relatively low resistance. It “transfers resistances.”

PHY 201 (Blum)10 Transistor etymology

PHY 201 (Blum)11 Totem Pole The right-hand side of the TTL inverter is an arrangement of transistors known as a totem pole. The transistors are arranged to that one is on and one is off. The inverter output is just above the lower transistor in the totem pole. – If the lower transistor is on, there is little voltage drop across the lower transistor and so the output voltage is close to 0 (ground).

PHY 201 (Blum)12 Totem Pole (Cont.) – If the lower transistor is off, then there is a large voltage drop across the lower transistor and so the output voltage is high. One is almost directly connected to the high or the ground giving this arrangement good power/stability characteristics.

PHY 201 (Blum)13 Similar arrangement/Opposite idea In the totem pole arrangement, one guarantees that one of the two transistors is on and the other is off – giving a low-resistance connection to high or low as the case may be. If we arrange for a third possibility that both transistors are off, then there is a high resistance between the output and both the high and the low. This high-resistance or high-impedance state is neither high nor low, but effectively disconnected.

PHY 201 (Blum)14 Poor Man’s TriState (Enabled Data Low)

PHY 201 (Blum)15 Poor Man’s TriState (Enabled Data High)

PHY 201 (Blum)16 Poor Man’s TriState (Not Enabled)

PHY 201 (Blum)17 Poor Man’s TriState (Not Enabled)

PHY 201 (Blum)18 Same idea as the tri-state buffer This circuit has the essential ingredients to make a tri-state buffer. Recall that tri-state buffers are used in conjunction with buses. When one has several devices that could place their information on the bus (“drive the bus”) only one of them should. – If two devices attempt to drive the bus to opposite voltage levels, there will be a short.

PHY 201 (Blum)19 Three State Logic AEOutput 00Z (High impedance)

PHY 201 (Blum)20 Tri-state buffer Compare the Electronics Workbench tri-state buffer to the previous circuit made of transistors and logic gates.

PHY 201 (Blum)21 In the high impedance state

PHY 201 (Blum)22 In the high impedance state

PHY 201 (Blum)23 In the “enabled” state

PHY 201 (Blum)24 In the “enabled” state

PHY 201 (Blum)25 Sequential Logic Whereas combinatorial logic depends only on the current inputs, sequential logic can also depend on the previous “state” of the system. Circuitry designed to hold a high or low state is known as a flip-flop. A flip-flop is the smallest unit of RAM – random access memory. Recall there are two basic categories of RAM: dynamic RAM (DRAM) and static RAM (SRAM).

PHY 201 (Blum)26 Flip Flops Flip-flops serve as the elementary units for memory in digital systems. Two features are needed: 1. The circuit must be able to “hold” either state (a high or low output) and not simply reflect the input at any given time. 2. But in some circumstances, we must be able to change (to “set” and “reset”) the values.

PHY 201 (Blum)27 Remembrance of states past The way in which the previous state information is held is different for different types of memory In DRAM (dynamic random access memory), the state (1 or 0) is held by a charge (or lack thereof) remaining on a capacitor – Charges tend to leak off of capacitors, which is why DRAM must be periodically refreshed

PHY 201 (Blum)28 Simple DRAM (Reset)

PHY 201 (Blum)29 Simple DRAM (Set)

PHY 201 (Blum)30 Simple DRAM (Hold)

PHY 201 (Blum)31 Simple DRAM (Hold)

PHY 201 (Blum)32 Simple DRAM (Reset)

PHY 201 (Blum)33 Simple DRAM (Hold)

PHY 201 (Blum)34 Simple DRAM (Hold)

Analog-to-Digital Converter ADC

PHY 202 (Blum)36 Simple Digital to Analog Converter.111 corresponds to 7/8 7/8 of 5 is 4.375

PHY 202 (Blum)37 Simple Digital to Analog Converter.100 corresponds to 1/2 1/2 of 5 is 2.5

PHY 202 (Blum)38 Analog-to-Digital We have seen a simple digital-to-analog converter, now we consider the reverse process For this purpose we introduce a new circuit element — the comparator A digital comparator would compare two binary inputs A and B and determine if A is larger than B (as well as if A = B). An analog comparator would determine whether voltage A is larger than voltage B

PHY 202 (Blum)39

PHY 202 (Blum)40 Comparator (analog) + Input higher than – input, output is high

PHY 202 (Blum)41 Comparator (analog) + Input lower than – input, output is low

PHY 202 (Blum)42 1-bit analog-digital converter Reference Voltage Input voltage Input voltage is less than half of reference voltage, result is low.

PHY 202 (Blum)43 1-bit analog-digital converter Reference Voltage Input voltage Input voltage is more than half of reference voltage, result is high.

PHY 202 (Blum)44 Toward a 2-bit analog-digital converter

PHY 202 (Blum)45 Toward a 2-bit analog-digital converter

PHY 202 (Blum)46 Toward a 2-bit analog-digital converter

PHY 202 (Blum)47 Toward a 2-bit analog-digital converter

Finish this truth table >3/4 Comparator >1/2 Comparator >1/4 Comparator ½’s place¼’s place PHY 202 (Blum)48 Doesn’t occur

PHY 202 (Blum)49 Integrated circuit version Warning: may need to flip switch back and forth.

PHY 202 (Blum) / 5 (in Scientific Mode)

PHY 202 (Blum)51 *2x^y8=

PHY 202 (Blum)52 Binary Mode

PHY 202 (Blum)53 Compare

PHY 202 (Blum)54 Scientific Mode

PHY 201 (Blum) Digital Comparators

PHY 201 (Blum) What is it? A comparator is circuitry that compares two inputs A and B, determining whether the following conditions are true or false – A = B – A > B – A < B – A  B – A  B – A  B

PHY 201 (Blum) Two will do Actually the first two will suffice, since the others are easily related to these – A B)) AND (NOT(A = B)) – A  B  (A > B) OR (A = B) – A  B  NOT(A > B) – A  B  NOT(A = B)

PHY 201 (Blum) One-bit comparator InputOutput AB=>

PHY 201 (Blum) Gate version

PHY 201 (Blum) Comparing word equality To compare if two words are equal, you pair up the bits holding the same position in each word, and each individual pair must be equal for the words to be equal. – 1100 and 1110  {(1,1), (1,1), (0,1), (0,0)} are not equal – 1100 and 1100  {(1,1), (1,1), (0,0), (0,0)} are equal

PHY 201 (Blum) Comparing word inequality Assume unsigned integers, then – If the most significant bit of word A is greater than the most significant bit of word B, then word A is greater than word B. – If the most significant bit of word A is less than the most significant bit of word B, then word A is less than word B. – If the most significant bit of word A is equal to the most significant bit of word B, then we must compare the next most significant bits.

PHY 201 (Blum) And so on If the most significant bits are equal, one compares the next-most significant bits. Then if the next most significant bits are equal, one compares the next-next-most significant bits, and so on. It seems that one must know the outcome of testing the more significant bits before one proceeds to the less significant bits.

PHY 201 (Blum) 4-bit comparator