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UNIT 1
REGISTER TRANSFER AND MICROOPERATIONS
Register Transfer Language Digital System : An interconnection of digital hardware modules that accomplish specific information-processing task. How Digital systems are built? Digital systems are built with digital modules. Those modules are connected with control and data paths. How Digital modules are built? Digital modules are built with digital components. Ex: registers, decoders, arithmetic elements and control logic. How Digital modules are defined? Digital modules are best defined by registers they contain and operations they perform on stored data. Micro operations : The operations executed on data stored in registers are called Micro-operations. An elementary operation performed in information stored in register(s). Ex: shift, count, clear, increment, load etc., How internal hardware organization of a digital computer is defined? Internal hardware organization of a digital computer is best defined by: Registers it contains and their functions Sequence of micro operations performed on data inside registers Control that ignites the sequence of micro operations Register transfer language: RTLis set of symbolic notations used to describe micro operations, transfer among registers. RTL is a system for expressing in symbolic form the micro operation sequences among registers in a digital module
Designation of Registers: Registers are designated by capital letters; sometimes followed by numbers to denote the function of a register. Examples: MAR for Memory Address Register PC for Program Counter IR for Instruction register The individual flip flops in n-bit register is numbered from 0 in right most to n-1 in left most. A register can be viewed as a single entity or may also be represented showing the bits of data they contain. Registers can be designated by a whole register, portion of a register, or a bit of a register. Register transfer: Basic symbols for register transfer : Register Transfer is defined as copying the content of one register to another. For register transfers, the data transfer from one register to another is designated in symbolic form by replacement operator.
Hardware Implementation for control function: R1 transfer to R2. Output of register R1is connected to n input of register R2. Register R2 has a load control activated by P control function and the whole operation is synchronized with the central clock. The rising edge of the CLK input triggers activates P at t time and at t+1 time the transfer takes place. Assume : Registers are comprised of D FF that acts on rising edge clocks. Simultaneous Operations: In cases where two or more operations are to occur simultaneously, they are separated with commas as shown next: P: R3 ๏R5, MAR๏IR If the control function P = 1, load the contents of R5 into R3, and at the same time (clock), load the contents of register IR into register MAR. Bus and Memory Transfer If we need to move data from and to multiple registers , problem arises. The number of wires will be so large if separate lines are used to connect all registers with each other. To completely connect n registers we need n(n-1) lines. So the cost is in order of O(n2). This is not a realistic approach to be used in a large digital system. The solution is to use a common โBusโ. New approach: Use one centralized set of circuits for data transfer the โbusโ. Also use control circuits to select which register is the source, and which is the destination.
Definition of a bus : Bus is a path (of a group of wires) over which information is transferred, from any of several sources to any of several destinations. One way of constructing a bus is by using multiplexers. The bus system will multiplex k registers of n bits each to produce an n-line common bus. The number of multiplexers need is n The size of each multiplexer is K x 1 Another way of constructing a bus is by using buffers or 3-state gates. Bus Transfer in RTL: The transfer of information from a bus into one of many destination registers can be accomplished by connecting bus lines to the inputs of all registers and activating load control of selected destination. The symbolic statement for a bus transfer may mention the bus or may be implied in the statement. R2 ๏ R OR BUS ๏ R1, R2 ๏ BUS Memory Transfer: Memory (RAM) can be thought as a sequential circuits containing some number of registers.
Read Operation : when address of required location is transferred into address register AR then the content is loaded into data register DR. DR ๏M[AR] Write operation: The content of data register DR is transferred into memory location addressed by address register AR. M[AR] ๏ DR Micro operations A micro operation is an elementary operation performed with data stored in register. Micro operations are classified into: Register transfer micro operation Arithmetic micro operation Logic micro operation Shift micro operation Basic arithmetic micro operations: Addition Subtraction Increment Decrement Arithmetic Shift The Add micro operation is specified as: R3 ๏R1 + R2. add content of R1 to R2 and store result of addition in R3. Usually it is implemented using hardware full adders. The Subtraction is usually implemented using complementation and addition R3 ๏ R1 + R2 +1 (R1 โ R2) i.e subtract R2 from R1 by adding the complement of R2 plus 1 to R1. It is implemented using a full adder a complement circuit.
Increment and decrement are implemented using Up and Down Counter. Multiplication and division are implemented using sequence of additions and subtractions respectively. Binary Adder: Binary adders are constructed from full adders connected in cascade. N-bit binary adder circuit need n number of full adders. Binary Adder-Subtractor: Subtraction of A โ B can be done by taking 2โs complement of B and added to A. The 2โs complement can be done by taking 1โs complement then adding โ1โ to the result. And finally the 1โs complement is the binary inversion. The addition and subtraction operations can be combined into one common circuit by including ExOR with each full adder. M control addition or subtraction operations. If M=0 then it is an adder And if M=1 then it is a subtractor.
Logic Micro operation : Logic micro operation specify binary operations on the strings of bits in registers. Logic micro operations are bit-wise operations, i.e., they work on the individual bits of data. These are useful for bit manipulations on binary data and also useful for making logical decisions based on the bit value. There are, in principle, 16 different logic functions that can be defined over two binary input variables. However, most systems only implement four of these: AND ( ), OR ( ), XOR ( ), Complement/NOT The others can be created from combination of these.
The hardware implementation of logic micro operation requires the insertion of the most important gates like AND, OR, EXOR, and NOT for each bit or pair of bits in the registers. one stage of a circuit: This circuit generates the four basic logic micro operations. It consists of four gates and a multiplexer. The two selection lines of the multiplexer selects one of the four logic operations available at one time. The circuit shows one stage for bit โiโ but for logic circuit of n bits the circuit should be repeated n times but with one remark; the selection pins will be shared with all stages.
Step 2: 0000 1010 A before 1001 0000 B (insert) (OR operation) 1001 1010 A after insertion Clear operation : compares the bits in A and B and produces an all 0โs result if the two number are equal. 1010 A 1010 B 0000 A โ A โ B Shift Micro operations : Shift micro-operations are used for serial transfer of data beside they are used in conjunction with arithmetic, logic, and other data processing operations. There are 3 types of shift micro operations. What differentiates them is the information that goes into the serial input: Logical shift Circular shift Arithmetic shift Logical Shift: Logical shift is one that transfers 0 through the serial input. In a Register Transfer Language, the following notation is used shl for a logical shift left shr for a logical shift right Examples: R2 ๏ shr R R3๏shl R Circular Shift:
The circular shift rotates of the register around the two ends without loss of information. This is accomplished by connecting the two ends of the shift register to each other. cil indicates circular shift left cir indicates circular shift right Circular shift right and left : Examples: R2 ๏ cir R R3 ๏ cil R Arithmetic Shift: Arithmetic shift is a micro-operation that shifts a signed binary number to the left or right. Arithmetic shift must leave sign bit unchanged. The arithmetic shift right is considered divide by 2 and left shift is considered multiply by 2. Arithmetic Shift Right & Left. Arithmetic shifts must leave the sign bit unchanged just to preserve the sign of the resulted number. If that case happened then it will be an overflow. An overflow flip flop will be used to detect arithmetic shift left overflow. In a RTL, the following notation is used for arithmetic shifts: ashl for an arithmetic shift left ashr for an arithmetic shift right Examples:
