Micro Operations in Computer Architecture

Micro Operations in Computer Architecture – A micro operation is an elementary operation executed on the information stored in one or more registers. A prespecified sequence of micro operations is performed on the stored information to complete a specified operation. The micro operations can be classified as follows:

1. Arithmetic micro operation
2. Logic micro operation
3. shift micro operation

Micro Operations

Arithmetic micro operations

Basic arithmetic micro operations are addition, subtraction, negation, increment, and decrement. Multiplication and division are also valid arithmetic operations, but not included in the basic set of micro operations. In most of the computer systems, the multiplication operation is implemented with a sequence of addition and shift micro operations. The division operation is implemented with a sequence of subtraction and shift micro operations. The table below shows the basic arithmetic micro operations.

Register transfer language	Description
R3 ← R1 + R2	Sum of R1 and R2 is copied to R3
R3 ← R1 – R2	Difference of R1 and R2 is copied R3
R3 ← R3 + 1	2’s complement the contents of R3 (negate)
R1 ← R1 + 1	Increment the contents of R1
R1 ← R1 – 1	Decrement the contents of R1

The above table shows that the basic micro operations are addition and subtraction. The increment and decrement micro-operations are symbolized by plus-one and minus-one operations, respectively. The following circuits can be used to implement various arithmetic micro-operations:

1. Binary Adder
2. Binary Adder/Subtraction
3. Binary Increments
4. Arithmetic Circuit

Binary Adder

The digital circuit that results in the arithmetic sum of two binary numbers of any length is called a binary adder. The binary adder can be designed with full adders connected serially. In such a type of design, the output carry of one full adder is transferred to the input carry of the next full adder. The figure below shows the 3-bit binary adder, which is constructed with 3 full adders.

Binary Adder/Subtractor

The subtraction of a binary number can be performed by taking the 2’s complement of the second number and adding it to the first number. The 2’s complement can be obtained by taking the 1’s complement and adding one to the least significant bit. Whereas the addition of binary numbers can be done by performing a direct addition operation as discussed in pervious section.

The addition and subtraction operations can be combined into a common circuit by including an Ex-OR gate with each full adder. A 3-bit adder/subtractor is shown in the figure below.

Mode selection input, as shown in the above figure, controls the operations. When mode selection input M=1, the circuit behaves as a subtractor, whereas for M=0, the circuit behaves as an adder.

Binary Incrementer

The binary increment micro operation is defined as the addition of one in a register. This can be achieved by means of half adders connected in a serial manner. The block diagram of a 3-bit binary incrementer is shown below.

Arithmetic Circuit

The basic arithmetic micro operations listed in the above table can be implemented in one composite arithmetic circuit. The basic component of an arithmetic circuit is the full adders with the multiplexer circuits. The 4-bit arithmetic circuit is shown in the figure below.

The 4-bit arithmetic circuit has four full adders to make a four-bit adder. Four 4:1 multiplexers are used to choose different operations. There are two 4-bit inputs (A and B) and one 4-bit output (D). Each bit of input B is connected to the corresponding Y input of the full adder through the multiplexer, whereas each bit of input A is connected directly to the X input of the full adder. The output of the circuit is calculated from the following arithmetic sum.

D = X+Y+C_in

Here, X input is always equal to A input wheres Y input can be B, B, 0, or 1 according to the selection lines (S₁ and S₀) of the multiplexer. C_in is the input carry, which can be equal to 0 or 1. By controlling the value of selection lines and input carry, it is possible to generate eight arithmetic micro operations shown in the table below.

S1	S0	Cin	Y	D = X+Y+Cin	Micro Operations
0	0	0	B	D = A + B	Addition
0	0	1	B	D = A + B + 1	Addition with carry
0	1	0	B	D = A + B	Subtraction with borrow
0	1	1	B	D = A + B + 1	Subtraction
1	0	0	0	D = A	Transfer A
1	0	1	0	D = A + 1	Increment A
1	1	0	1	D = A – 1	Decrement A
1	1	1	1	D = A	Transfer A

When S₁ S₀ = 00, the output of the multiplexer is B and applied to the Y input of the full adder. if C_in = 0, the output D = A+B+0 (addition) and if C_in = 1, the output D = A+B+1 (addition with carry).

When S₁ S₀ = 01, the output of the multiplexer is B and applied to the Y input of the full adder. if C_in = 0, the output D = A+B+0 = A+(B+1)-1 = A + (2’s complement of B) – 1 = A-B-1 (subtraction with borrow) and if C_in = 1, the output D = A+B+1 = A+(2’s complement of B) = A-B (subtraction).

When S₁ S₀ = 10, the outputs of all multiplexers are 0 and applied to the Y inputs of all full adders. In C_in = 0, the output D=A + (0000)₂ +0 = A (Transfer) and if C_in=1, the output D=A+(0000)₂+1 = A+1 (Increment).

When S₁ S₀ = 11, the outputs of all multiplexers are 1 and applied to the Y inputs of all full adders. If C_in = 0, the output D=A+(1111)₂+0=A+(1’s complement of 0) + 1-1 = A+(2’s complement of 0)-1=A-0-1=A-1 (Decrement) and if C_in = 1, the output D=A+(1111)₂+1 = A+(1’s complement of 0)+1=A+(2’s complement of 0) = A-0=A(Transfer).

Note – The micro operation D = A (transfer) is generated twice, so there are only seven distinct micro operations in the arithmetic circuit.

Logic Micro Operations

The logic micro operations include the basic operations like AND, OR, EX-OR, NOT, etc. These operations consider each bit of the register separately and treat it as a binary variable. It means logic micro operations are bit-wise micro operations. If there are two binary variables, 16 different logic micro operations can be performed on them.

The sixteen logic micro operations are derived from the truth table of logic functions, as shown in the table below. The bit-wise variables are represented by x (contents of register A) and y (Contents of register B). Each bit of the register is considered as a binary variable is micro operation is performed on the string of bits stored in the registers. All sixteen logic micro operations are shown in the table below.

Hardware Implementation (Logic Circuit)

Although there are sixteen logic micro-operations listed in the above table, most of the digital systems use only four micro operations (AND, OR, Ex-OR and complement). Other micro operations can be derived from the combination of these four. One stage of a logic circuit is shown in the figure below.

S1	S0	Output	Operation
0	0	F = A ∧ B	AND
0	1	F = A ∨ B	OR
1	0	F = A⊕B	Ex-OR
1	1	F ← A	Complement

1. When S₁S₀=00, the input I₀ will be at the output of the multiplexer. Hence F_i=I₀=A_i ∧ B_i (AND).
2. When S₁S₀=01, the input I₁ will be at the output of the multiplexer. Hence F_i=I₁=A_i ∧ B_i (OR).
3. When S₁S₀=10, the I₂ input will be available at the output of the multiplexer. Hence F_i=A_i ⊕ B_i (Ex-OR).

In the same manner, when S₁S₀=11, I₃, the input will be at the output of the multiplexer. Hence F_i=A (complement of A).

Logic Circuit Application

The logic micro operations are executed on the individual bits of the data stored in the register. The logic micro operations are rarely used in scientific computations, but they are useful for bit manipulation of binary data and for making logical decisions. It means that logic micro operations can be used to change bit values, delete a group of bits, or insert new bit values into a register. Therefore, a logic circuit can be used for the following operations.

1. Selective Set
2. Selective Reset
3. Selective Complement
4. Selective Insert

Selective Set – The selective set operation sets (makes high) the selected bits of a register. Consider a register A that contains the data. This operation sets the bits in register A where there are corresponding 1’s in register B. It does not affect bit positions that have 0’s in register B. The truth table for the selective set operation is given in the table below.

Bit of Register A (Before)	Corresponding Bit of Register B	Bit of Register A (After)	Operation
0	0	0	No Change
0	1	1	Set
1	0	1	No Change
1	1	1	Set

From the above truth table, it can be noticed that the bits of register A after the operation are obtained from the logic-OR operation of bits in register B and the previous values of register A. Therefore, the OR micro operation can be used to selectively set bits of a register.

Numeric example:

10110110 – Register A (Before)
01101110 – Register B
————————
11111110 – Register A (After)
———————–

Selective Reset (Mask) – The selective reset operation resets (makes low) the selected bits of a register. Consider a register that contains the original data. This operation resets the bits in register A where there are corresponding 0’s in register B. It does not affect bit positions in register A that have corresponding 1’s in register B. The truth table for the selective reset operation is shown in the table below.

Bit of Register A (Before)	Corresponding Bit of Register B	Bit of Register A (After)	Operation
0	0	0	Reset
0	1	0	No change
1	0	0	Reset
1	1	1	No change

From the above truth table, it can be noticed that the bits of register A after the operation are obtained from the logic-AND operation of bits in register B and the previous values of register A. Therefore, the AND micro operation can be used to selectively set bits of a register.

Numeric example:

10110110 – Register A (Before)
01101110 – Register B
————————
00100110 – Register A (After)
———————–

Selective Complement – The selective complement operation complements the selected bits of a register. Consider a register A that contains the data. This operation complements the bits of register A where there are corresponding 1’s in register B. It does not make any change to the bit positions that have 0’s in register B. The table below shows the truth table for the selective complement operation.

Bit of Register A (Before)	Corresponding Bit of Register B	Bit of Register A (After)	Operation
0	0	0	No change
0	1	1	Complement
1	0	1	No change
1	1	0	Complement

It can be seen from the above truth table that the bits of register A after the operation are obtained from the logic Exclusive-OR operation of bits in register B and previous values in register A. Therefore, the Ex-OR micro operation can be used to selectively complement bits of a register.

Numeric example:

1011 0110 – Register A (Before)
0110 1110 – Register B
————————
0010 0110 – Register A (After)
———————–

Selective Insert – The selective insert operation inserts a new value into a group of bits. This operation is a combination of selective reset and selective set operations. This is performed by first selective reset the bits, and selective set them with the required value.

Numeric example: – Let, in a group of eight bits (stored in register A), four most significant bits are required to be 1001.

Step-I

1011 0110 – Register A (Before)
0000 1111 – Register B
————————
0000 0110 – Register A (After selective reset)
———————–

Step-II

0000 0110 – Register A (Before)
1001 0000 – Register B
————————
1001 0110 – Register A (After selective reset)
———————–

Shift Micro Operation

Shift micro operations are used for serial transfer of data. The contents of a register can be shifted to the left or to the right in different ways. There are three types of shifts:

1. Logical Shift
2. Circular Shift
3. Arithmetic Shift.

Logical Shift

The logical shift inserts 0 through the serial input. The symbols shl (Shift left) and shr (Shift right) are used. The figure shows examples of logical shift.

The above two micro operations specify a 1-bit shift to the left of the contents of register A and a 1-bit shift to the right of the contents of register B. The bit inserted into the end position is to be 0 during logical shift.

Circular Shift

The circular shift rotates the bits of the register around the two ends without loss of information. This is also known as the rotate operation. Symbols cil (circular left shift) and cir (circular right shift) are used for circular shift. The figure below shows an example of circular shift.

The above micro operations circulate the contents of register A in the left direction (1-bit) and the contents of register B in the right direction (1-bit) without loss of information. In circular left shift, the most significant bit will be copied to the least significant bit position, whereas in circular right shift, the least significant bit will be copied to the most significant bit position.

Arithmetic Shift

An arithmetic shift is a micro operation 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. The sign of the number remains unchanged after an arithmetic shift. The symbols ashl (arithmetic shift left) and ashr (arithmetic shift right) are used for arithmetic shift. The examples of arithmetic shift are shown in the figure below.

The above micro operation shows in the figure perform arithmetic shift left to the contents of register A. This inserts a 0 into A₀ and shifts all other bits to the left. If An-1 and An-2 are not the same, an error may occur. In the micro operation shown in the above figure, the arithmetic shift leaves the sign bit unchanged, and the same B_n-2 receives the bit from B_n-1, and so on. The bit in B₀ is lost.

Hardware Implementation (shifter Circuit)

RTL	Micro Operation	Description
A ← shl A	Shift left register A	Contents of A shift left by 1-bit position. A ‘0’ is inserted at right most bit. Left most bit is lost.
A ← shr A	Shift right register A	Contents of A shift right by 1-bit position. A ‘0’ is inserted at left most bit. Right most bit is lost.
A ← cil A	Circular shift left register A	Contents of register A are circularly shifted right by 1-bit position, the right-most bit goes into left most bit.
A ← cir A	Circular shift right register A	Shifts the contents of A left by 1-bit position. ‘0’ is inserted at the right-most bit position, and the sign bit receives the most significant bit.
A ← ashl A	Arithmetic shift left register A	Shifts the contents of A left by 1-bit position. ‘0’ is inserted at the right-most bit position, the sign bit receives the most significant bit.
A ← ashr A	Arithmetic shift right register A	Shifts contents of A right by 1-bit position. The sign bit is circulated in at the leftmost bit position.

The shift micro operations given in the above table can be implemented using the circuit shown in the figure below. This is a 4-bit shifter, which has four data inputs A₀ to A₃, and four data outputs F₀ to F₃. There are two serial inputs, one for shift left (I_L) and the other for shift right (I_R).

When S=0, the input data are shifted right, and when S=1, the input data are shifted left. The function table is also shown in the figure below.

Select Input (S)	Output F0	Output F1	Output F2	Output F3
0 (Shift right)	IR	A0	A1	A2
1 (Shift left)	A1	A2	A3	IL

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