Memory

Memory is a collection of cells, each with a unique physical address. We use the generic word cell here rather than byte, because the number of bits in each addressable location, called the memory's addressability, varies from one machine to another. Today, most computers are byte addressable.

To fully illustrate the concept of memory, take a computer with 4GB of RAM as an example. The memory consists of 4 × 2³⁰ bytes, which means each byte of the computer is uniquely addressable, and the addressability of the machine is 8 bits. The cells in memory are numbered consecutively beginning with 0. For example, if the addressability is 8, and there are 256 cells of memory, the cells would be addressed as follows:

Address	Contents
00000000	11100011
00000001	01010101
${\displaystyle \vdots }$	${\displaystyle \vdots }$
11111100	00000000
11111101	11111111
11111110	10101010
11111111	00110011

What are the contents of address 11111110? The bit pattern stored at that location is 10101010. However, what the contents actually represents, be it instructions, value, sign, etc. will be discussed later. What is important, however, is to understand that the bit pattern is information and can be interpreted.

When referring to the bits in a byte or word, the bits are numbered from right to left beginning with zero. The bits in address 1111110 are numbered as follows:

Arithmetic/Logic Unit

The Arithmetic/Logic Unit (ALU) is capable of performing basic arithmetic operations such as adding, subtracting, multiplying, and dividing two numbers. This unit is also capable of performing logical operations such as AND, OR, and NOT. The ALU operates on words, a natural unit of data associated with a particular computer design. Historically, the word length of a computer has been the number of bits processed at once by the ALU. However, the current Intel line of processors has blurred this definition by defining the word length to be 16 bits. The processor can work on words (of 16 bits), double words (32 bits), and quadwords (64 bits). In the rest of this wiki, when referring to word, it will be of the historical nature aforementioned.

Most modern ALUs have a small number of special storage units called Registers. These registers contain one word and are used to store information that is needed again immediately. For example, in the calculation of 1 × (2 + 3). 2 is first added to 3 and the result is multiplied by 1. Rather than storing the result of adding 2 and 3 in memory and then retrieving it to multiply it by 1, the result is left in a register and the contents of the register is multiplied by 1. Access to registers is much faster than access to memory locations.

Input/Output Units

All of the computing power in the world would not be useful if one could not input values into the calculations from the outside or report to the outside the results of said calculations. Input and output units are the channels through which the computer communicates with the outside world.

An Input Unit is a device through which data and programs from the outside world are entered into the computer. The first input units interpreted holes punched on paper tape or cards. Modern-day input devices, however, include, but are not limited to; keyboards, mice, cameras (also known as, simply, webcams), and scanning devices.

An Output Unit is a device through which results stored in the computer memory are made available to the outside world. Examples include printers and screen monitors.

Control Unit

The Control Unit is the organising force in the computer, for it is in charge of the Fetch-Execute Cycle. There are two special registers in the control unit. The Instruction Register (IR) contains the instruction that is being executed, and the Program Counter (PC) contains the address of the next instruction to be executed. Because the ALU and the control unit work so closely together they are often thought of as one unit called the Central Processing Unit (CPU).

Above is a simplified view of the flow of information through the parts of a von Neumann machine. The parts are connected to one another by a collection of wires called a bus, through which data travels in the computer. Each bus carries three kinds of information; address, data, and control. An address is used to select the memory location or device to which data will go, or from which it will be taken. Data then flows over the bus between CPU, memory, and I/O Devices. The control information is used to manage the flow of addresses and data. For example, a control signal will typically be used to determine the direction in which the data is flowing either to or from the CPU. The Bus Width is the number of bits that it can transfer simultaneously. The wider the bus, the more address or data bits it can move at once.

Because memory accesses are very time consuming relative to the speed of the processor, many architectures provide Cache Memory. Cache memory is a small amount of fast-access memory into which copies of frequently used data are stored. Before a main memory access is made, the CPU checks whether the data is stored in the cache memory. Pipelining is another technique used to speed up the Fetch-Execute Cycle. This technique splits an instruction into smaller steps that can be overlapped.

In a personal computer, the component in a von Neumann machine reside physically a printed circuit board called the Motherboard. The motherboard also has connections for attaching other devices to the bus, such as a mouse, a keyboard, or additional storage devices.

So what does it mean to say that a machine is an n-bit processor? The variable n usually refers to the number of bits in the CPU general registers: Two n-bit numbers can be added with a single instruction. It also can refer to the width of the bus, which is the size of the addressable memory—but not always. In addition, n can refer to the width of the data bus—but not always.

Fetch the Next Instruction

The PC increments one by one to point to the next instruction to be executed, so the control unit goes to the address in the memory address register which holds the address of the next instruction specified in the PC, takes it to the main memory through the address bus and returns it to the memory buffer register via the data bus. The MBR is a two way register that temporarily holds data fetched from the Memory(cache or RAM), makes a copy of the contents, and places the copy in the IR. At this point the IR contains the instruction to be executed. Before going to the next step in the cycle, the PC must be updated to hold the address of the next instruction to be executed when the current instruction has been completed. There after the instruction register is responsible for the instruction to be solved by the CU. the CU checks on the status of the instruction and then allows execution. Because the instructions are stored contiguously in memory, adding the number of bytes in the current instruction to the PC should put the address of the next instruction into the PC. Thus the control unit increments the PC. It is possible that the PC may be changed later by the instruction being executed.

In the case of an instruction that must get additional data from memory, the ALU sends an address to the memory bus, and the memory responds by returning the value at that location. In some computers, data retrieved from memory may immediately participate in an arithmetic or logical operation. Other computers simply save the data returned by the memory into a register for processing by a subsequent instruction. At the end of execution, any result from the instruction may be saved either in registers or in memory.

Decode the Instruction

To execute the instruction in the instruction register, the control unit has to determine what instruction it is. It might be an instruction to access data from an input device, to send data to an output device, or to perform some operation on a data value. At this phase, the instruction is decoded into control signals. That is, the logic of the circuitry in the CPU determines which operation is to be executed. This step shows why a computer can execute only instructions that are expressed in its own machine language. The instructions themselves are literally built into the circuit.

Get Data If Needed

The instruction to be executed may potentially require additional memory accesses to complete its task. For example, if the instruction says to add the contents of a memory location to a register, the control unit must get the contents of the memory location.

Execute the Instruction

Once an instruction has been decoded and any operands (data) fetched, the control unit is ready to execute the instruction. Execution involves sending signals to the arithmetic/logic unit to carry out the processing. In the case of adding a number to a register, the operand is sent to the ALU and added to the contents of the register.

When the execution is complete, the cycle begins again. If the last instruction was to add a value to the contents of a register, the next instruction probably says to store the results into a place in memory. However, the next instruction might be a control instruction—that is, an instruction that asks a question about the result of the last instruction and perhaps changes the contents of the program counter.

Hardware has changed dramatically in the last half-century, yet the von Neumann model remains the basis of most computers today. As Alan Perlis, a well-known computer scientist once said;

Sometimes I think the only universal in the computing field is the Fetch-Execute Cycle.

—Alan Perlis, 1981.

Single Contiguous Memory Management

Has only the operating system and one other program in memory at one time. This is the most basic type of memory management.

Partition Memory Management

The memory is broken up into different parts. Has the operating system and any number of programs running at the same time through these different partitions. The partitions have a base and a bound register.

Base register

• A register that holds the beginning address of the current partition (the one that is running)

Bounds register

• A register that holds the length of the current partition

Partition selection First fit

• Allocate program to the first partition big enough to hold it

Best fit

• Allocated program to the smallest partition big enough to hold it

Worst fit

• Allocate program to the largest partition big enough to hold it

Paged Memory Management

A technique in which processes are divided into fixed-size pages and stored in memory frames when loaded.

Frame

• A fixed-size portion of main memory that holds a process page

Page

• A fixed-size portion of a process that is stored into a memory frame

NOT Gate

Boolean Expression	Logic Diagram Symbol	Truth Table
X = A'	AX	A X 0 1 1 0

A NOT gate accepts one input value and produces one output value. The table to the right illustrates a NOT gate in three ways; as a Boolean expression, as its logical diagram symbol, and using a truth table. In each representation, the variable A represents the input signal, which is either 0 or 1. The variable X represents the output signal, whose value (0 or 1) is determined by the value of A.

By definition, if the input value for a NOT gate is 0, the output is 1; if the input value is 1, the output is 0. A NOT gate is sometimes referred to as an inverter because it inverts the input value.

In Boolean expressions, the NOT operation is represented by the ' mark after the value begin negated. Sometimes this operation is shown as a horizontal bar over the value begin negated. In the Boolean expression in the table, X is assigned to the value determined by applying a NOT operation to input value A. In such an assignment statement, the variable on the left of the equal sign takes on the value of the expression on the right-hand side.

The logical diagram symbol for a NOT gate is a triangle with a small circle (called an inversion bubble) on the end. The input and output are shown as lines flowing into and out of the gate. Sometimes these lines are labeled, though not always.

The truth table shows all possible input values for a NOT gate as well as the corresponding output values. Because there is only one input signal to a NOT gate, and that signal can only be 0 or 1, there are only two possibilities for the column labelled A in the truth table. The column labelled X shows the output of the gate, which is the inverse of the input. Note that of the three representations, only the truth table actually defines the behaviour of the gate for all situations.

These three notations are just different ways of representing the same thing, for example, the result of the Boolean expression 0' is always 1, and the result of the Boolean expression 1' is always 0. This behaviour is consistent with the values shown in the truth table.

AND Gate

Boolean Expression	Logic Diagram Symbol	Truth Table
X = A • B	A X B	A B X 0 0 0 0 1 0 1 0 0 1 1 1

Unlike the NOT gate, which accepts one input signal, an AND gate accepts two input signals. The values of both input signals determine what the output signal will be. If the two input values for an AND gate are both 1, the output is 1; otherwise, the output is 0.

The AND operation in Boolean algebra is expressed using a single dot (•) or, in some cases, an asterisk (*). Often the operator itself is assumed, for example A•B is often written as AB.

Because there are two inputs and two possible values for each input, four possible combinations of 1 and 0 can be provided as input to an AND gate. Therefore, four situations can occur when the AND operator is used in a Boolean expression.

Likewise, the truth table showing the behaviour of the AND gate has four rows, showing all four possible input combinations.

OR Gate

Boolean Expression	Logic Diagram Symbol	Truth Table
X = A + B	A X B	A B X 0 0 0 0 1 1 1 0 1 1 1 1

Like the AND gate, there are two inputs to an OR gate. If the two input values are both 0, the output value is 0; otherwise, the input is 1.

The Boolean algebra OR operation is expressed using a plus sign (+). The OR gate has two inputs, each of which can be one of two values, so as with an AND gate there are four input combinations and therefore four rows in the truth table.

XOR Gate

Boolean Expression	Logic Diagram Symbol	Truth Table
X = A ⊕ B	A X B	A B X 0 0 0 0 1 1 1 0 1 1 1 0

The XOR, or exclusive OR, gate is illustrated to the right. An XOR gate produces 0 if its two inputs are the same, and 1 otherwise. Note the difference between the XOR gate and the OR gate; they differ only in one input situation. When both input signals are 1, the OR gate produces a 1 and the XOR produces a 0.

Sometimes the regular OR gate is referred to as the inclusive OR, because it produces a 1 if either or both of its inputs is a 1. The XOR produces a 1 only if its inputs are mixed, one 1 and one 0. Think of XOR gates as saying, "When I say or, I mean one or the other, no both."

The Boolean algebra symbol ⊕ is sometimes used to express the XOR operation. However, the XOR operation can also be expressed using the other operators; we leave that as an exercise.

Note that the logic diagram symbol for the XOR gate is just like the symbol for an OR gate except that it has an extra curved line connecting its input signals.

NAND and NOR Gates

NAND Gate
Boolean Expression	Logic Diagram Symbol	Truth Table
X = (A • B)'	A X B	A B X 0 0 1 0 1 1 1 0 1 1 1 0
NOR Gate
Boolean Expression	Logic Diagram Symbol	Truth Table
X = (A + B)' X = A - B	A X B	A B X 0 0 1 0 1 0 1 0 0 1 1 0

The NAND and the NOR gate accept two input values. The NAND and NOR gates are essentially the opposite of the AND and OR gates, respectively. That is, the output of a NAND gate is the same as if one took the output of an AND gate and put it through an inverter (a NOT gate).

There are typically no specific symbols used to express the NAND and NOR gates operations in Boolean algebra. Instead, one should rely on their definitions to express the concepts. That is, the Boolean algebra expression for NAND is the negation of the AND operation. Likewise, the Boolean algebra expression for NOR is the negation of an OR operation.

The logic diagram symbols for the NAND and NOR are the same as those for the AND and OR except that the NAND and NOR symbols have the inversion bubble (to indicate the negation). Compare the output columns for the truth tables for the AND and NAND. They are the opposite, row by row. The same is true for OR and NOR gates.

Combinational Circuits

A combinational circuit consists of logic gates whose outputs are determined at any time from the present combination of inputs irrespective of previous inputs.It consists of input variables, logic gates and output variables. The logic gate accept signals from inputs and generate signals at the outputs.Some of the examples of combinational circuits are binary adder,decimal adder,decoder,multiplexer,half adder, half subtractor etc.

Arithmetic circuits

Adders

Half adder

A half-adder circuit diagram

A logic circuit for the addition of two one-bit numbers is called a half adder. There must be two bits output: the sum of the addition (either a 1 or 0) and whether or not you carry a bit. The carry comes from the addition of 1 + 1, which equals 10 (binary 2). The addition process is reproduced in this truth table.

Multiplexers

BOOLEAN EXPRESSION:
D0 = X’Y’  ,  D1 = X’Y
D2 = XY’  ,  D3 = XY