Digital Logic Structures MOS transistors logic gates functional units of a computer

MOS: Metal-oxide Semiconductor Basic electrical circuit: power supply, switch, lamp manipulating the switch makes/breaks the circuit

2 Basic Types of Transistors N-type: acts as a closed circuit when given a logically high voltage P-type: acts as a closed circuit when given a logically low voltage Circuits with both are called CMOS gate

Logic Gates basic logic structures (AND, OR, NOT) are created out of CMOS transistors inverter: recall the truth table for NOT inout inout in out

OR and NOR gates given the circuit, build the truth table how do we get OR?

AND and NAND gates Construct NAND first, just as with NOR NAND and NOR technology very widely used

Inverter AND, NAND OR, NOR a single bubble on an input or output denotes an inverter multiple-input gates Notation for Digital Logic Gates

Expressions to Truth Tables NOT ((NOT A) or B) (A or B)

Expressions to Truth Tables NOT ((NOT A) or B) (A or B) AABORC

DeMorgan’s Laws A AND B = A OR B A OR B = A AND B

Logic Structures we build logic structures out of logic gates logic structures are components of the microarchitecture of a computer 2 kinds of logic structures some store information some do not store information

Combinational Logic Structures output is completely determined by the combination of input values examples: decoder multiplexor (MUX) full adder

Decoder outputs one 1 and the rest 0s where the 1 corresponds to a unique input pattern for n inputs lines, 2 n output lines the output line that has the value 1 is asserted

MUX selects an input and connects it to the output for 2 n inputs lines, n select lines MUX is represented by an upside down trapezoid

4 Input MUX

Single Bit Adder a b c i c o s

4bit Adder

Logical Completeness we can build a circuit for any truth table using AND, OR, and NOT proof by construction: draw vertical lines for all inputs for each 1 in the output value, connect 1s in the input directly to an AND gate (invert 0s); repeat for each row OR all of the AND gates together

Basic Storage Elements R-S latch: simple structure that stores 1 bit of information implemented with NAND gates start with quiescent state (R=S=1) as long as ‘a’ is 1, it stays 1 (same for 0)

Reset/Set the Latch put 0 on S while R=1, causes ‘a’ to become 1 put 0 on R while S=1, causes ‘a’ to become 0 behavior is undefined if both go to 010 1 0  1 1010 quiescent

The Gated D-latch uses the R-S latch, plus some additional logic gates D is the value that is stored, but it is only set/reset when WE (write-enable) is 1 D’s value causes one of R or S to become 0 0101 0 1111 1010 1010 0101

Register every computer offers a number of registers: high speed special memory locations some registers have special meaning (e.g., PC is the program counter) note that outputs in the 4-bit register are labeled by Q(n-1:0)

Memory memory location: collection of bits, has to be uniquely identified identified by an address the number of bits we have to represent addresses determines the maximum number of locations that can be accessed in memory 2 24 = 16,777,216 = 16MB locations

Addressibility the number of bits we have to represent the data gives the addressibility of the memory. E.g. The size of each memory location. byte addressibility: convenient since characters are one byte supercomputers may be 64-bit addressible for 64-bit floating point numbers

2 2 by 3 Memory Address Decoding Logic Gated D-Latches 3-bit Value to be stored 4 Rows 4 memory Locations Trace how data is output and stored

Preview of the LC-2 memory registers Data (R0…R7, MDR, …) Control (PC, MAR, ….) multiplexers (MUXs) Arithmetic Logic Unit (ALU) Arithmetic operations (add, subtract) Bitwise logical operations (or, and,..)