Shift Micro-operations - logical, circular, arithmetic shifts




Shift rnicrooperations are used for serial transfer of data. They are also used in conjunction with arithmetic, logic, and other data-processing operations. The contents of a register can be shifted to the left or the right. At the same time that the bits are shifted, the first flip-flop receives its binary information from the serial input. During a shift-left operation the serial input transfers a bit into the rightmost position. During a shift-right operation the serial input transfers a bit into the leftmost position. The information transferred through the serial input determines the type of shift. There are three types of shifts: logical, circular, and arithmetic.

Logical shift: A logical shift is one that transfers 0 through the serial input. We will adopt the symbols shl and shr for logical shift-left and shift-right rnicrooperations. For example:

R1 ←  shl R1

R2 ← shr R2

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are two rnicrooperations that specify a 1-bit shift to the left of the content of register R 1 and a 1-bit shift to the right of the content of register R2. The register symbol must be the same on both sides of the arrow. The bit transferred to the end position through the serial input is assumed to be 0 during a logical shift.

 

The circular shift (also known as a rotate operation) circulates the bits of the register around the two ends without loss of information. This is accomplished by connecting the serial output of the shift register to its serial input. We will use the symbols cil and cir for the circular shift left and right, respectively. The symbolic notation for the shift rnicrooperations is shown in Table 4-7.

Shift Micro-operations - logical, circular, arithmetic shifts

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An arithmetic shift is a rnicrooperation that shifts a signed binary number to the left or right. An arithmetic shift-left multiplies a signed binary number by 2. An arithmetic shift-right divides the number by 2. Arithmetic shifts must leave the sign bit unchanged because the sign of the number remains the same

Shift Micro-operations - logical, circular, arithmetic shifts

when it is multiplied or divided by 2. The leftmost bit in a register holds the sign bit, and the remaining bits hold the number. The sign bit is 0 for positive and 1 for negative. Negative numbers are in 2's complement form. Figure 4-11 shows a typical register of n bits. Bit Rn- 1 in the leftmost position holds the sign bit. Rn-2 is the most significant bit of the number and Ro is the least significant bit. The arithmetic shift-right leaves the sign bit unchanged and shifts the number (including the sign bit) to the right. Thus Rn-1 remains the same, Rn-2 receives the bit from Rn-1 and so on for the other bits in the register. The bit in Ro is lost.

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The arithmetic shift-left inserts a 0 into R0 and shifts all other bits to the left. The initial bit of Rn-1 is lost and replaced by the bit from Rn-2. A sign reversal occurs if the bit in Rn-1 changes in value after the shift. This happens if the multiplication by 2 causes an overflow. An overflow occurs after an arithmetic shift left if initially, before the shift, Rn-1 is not equal to Rn-2. An overflow flip-flop Vs can be used to detect an arithmetic shift-left overflow.

Vs = Rn-1 + Rn-2

If Vs = 0, there is no overflow, but if Vs = I, there is an overflow and a sign reversal after the shift. Vs must be transferred into the overflow flip-flop with the same clock pulse that shifts the register.

 

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Hardware implementation

A possible choice for a shift unit would be a bidirectional shift register with parallel load (see Fig. 2-9). Information can be transferred to the register in parallel and then shifted to the right or left. In this type of configuration, a clock pulse is needed for loading the data into the register, and another pulse is needed to initiate the shift. In a processor unit with many registers it is more efficient to implement the shift operation with a combinational circuit. In this way the content of a register that has to be shifted is first placed onto a common bus whose output is connected to the combinational shifter, and the shifted number is then loaded back into the register. This requires only one clock pulse for loading the shifted value into the register.

shifter:

A combinational circuit shifter can be constructed with multiplexers as shown in Fig. 4-12. The 4-bit shifter has four data inputs, A0 through A3 and four data outputs, H0 through H3. There are two serial inputs, one for shift left (IL) and the other for shift right (h).

Shift Micro-operations - logical, circular, arithmetic shifts

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When the selection input S = 0, the input data are shifted right (down in the diagram). When S = 1, the input data are shifted left (up in the diagram). The function table in Fig. 4-12 shows which input goes to each output after the shift. A shifter with n data inputs and outputs requires n multiplexers. The two serial inputs can be controlled by another multiplexer to provide the three possible types of shifts.



Frequently Asked Questions

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Ans: The selective-set operation sets to 1 the bits in register A where there are corresponding 1's in register B. It does not affect bit positions that have D's in B. The following numerical example clarifies this operation. view more..
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Ans: Logic microoperations are very useful for manipulating individual bits or a portion of a word stored in a register. They can be used to change bit values, delete a group of bits, or insert new bit values into a register. view more..
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Ans: The hardware implementation of logic rnicrooperations requires that logic gates be inserted for each bit or pair of bits in the registers to perform the required logic function. Although there are 16 logic rnicrooperations, most computers use only four-AND, OR, XOR (exclusive-OR), and complementfrom which all others can be derived. view more..
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Ans: Shift rnicrooperations are used for serial transfer of data. They are also used in conjunction with arithmetic, logic, and other data-processing operations. The contents of a register can be shifted to the left or the right. At the same time that the bits are shifted, the first flip-flop receives its binary information from the serial input view more..
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Ans: Instead of having individual registers performing the microoperations directly, computer systems employ a number of storage registers connected to a common operational unit called an arithmetic logic unit, abbreviated ALU. view more..
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Ans: In this chapter we introduce a basic computer and show how its operation can be puter specified with register is defined by its internal transfer registers, statements. the limirlg The otganization and control of structure, the comand the set of instructions that It uses. The design of the computer is then carried out in detall. Although the basic computer presented in this chap view more..
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Ans: An instruction code is a group of bits that instruct the computer to perform a specific operation. It is usually divided into parts, each having its own particular interpretation. The most basic part of an instruction code is its operation part. The operation code of an instruction is a group of bits that define such operations as add, view more..
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Ans: The simplest way to organize a computer is to have one processor register and an instruction code format with two parts. The first part specifies the operation to be performed and the second specifies an address. The memory address tells the control where to find an operand in memory. This operand is read from memory and used as the data to be operated on together with the data stored in the processor register view more..
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Ans: In this chapter we introduce a basic computer and show how its operation can be puter specified with register is defined by its internal transfer registers, statements. the limirlg The otganization and control of structure, the comand the set of instructions that It uses. The design of the computer is then carried out in detall. Although the basic computer presented in this chapter is very small compared to commercial computers, It has the advantage of being simple enough so we can demonstrate the design process without too many complications. view more..
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Ans: It is sometimes convenient to use the address bits of an instruction code not as an address but as the actual operand. When the second part of an instruction code specifies an operand, the instruction is said to have an immediate operand. view more..
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Ans: Computer instructions are normally stored in consecutive memory locations and are executed sequentially one at a time. The control reads an instruction from a specific address in memory and executes it. It then continues by reading the next instruction in sequence and executes it, and so on. view more..
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Ans: The memory address register (AR) has 12 bits since this is the width of a memory address. The program counter (PC) also has 12 bits and it holds the address of the next instruction to be read from memory after the current instruction is executed. The PC goes through a counting sequence and causes the computer to read sequential instructions previously stored in memory. Instruction words are read and executed in sequence unless a branch instruction is encountered. view more..
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Ans: The basic computer has eight registers, a memory unit, and a control unit. Paths must be provided to transfer information from one register to another and between memory and registers. view more..
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Ans: The input data and output data of the memory are connected to the common bus, but the memory address is connected to AR. Therefore, AR must always be used to specify a memory address. By using a single register for the address, we eliminate the need for an address bus that would have been needed otherwise. The content of any register can be specified for the memory data input during a write operation. Similarly, any register can receive the data from memory after a read operation except AC . view more..
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Ans: The basic computer has three instruction code formats, as shown in Fig. 5-5. Each format has 16 bits. The operation code (opcode) part of the instruction contains three bits and the meaning of the remaining 13 bits depends on the operation code encountered. view more..
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Ans: Before investigating the operations performed by the instructions, let us discuss the type of instructions that must be included in a computer. A computer should have a set of instructions so that the user can construct machine language programs to evaluate any function that is known to be computable. The set of instructions are said to be complete if the computer includes a sufficient number of instructions in each of the following categories: view more..
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Ans: The timing for all registers in the basic computer is controlled by a master clock generator. The clock pulses are applied to all flip-flops and registers in the system, including the flip-flops and registers in the control unit. The clock pulses do not change the state of a register unless the register is enabled by view more..
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Ans: The last three waveforms in Fig. 5-7 show how SC is cleared when D3T4 = I. Output D3 from the operation decoder becomes active at the end of timing signal T2• When timing signal T4 becomes active, the output of the AND gate that implements the control function D3T4 becomes active. This signal is applied to the CLR input of SC. view more..




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