Micro Operations | 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. hift micro operation

Micro Operations

Arithmetic micro operations

Basic arithmetic micro operations are addition, subtraction, negate, 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. below table 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

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. 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 the arithmetic sum of two binary number of any length is called binary adder. The binary adder can be designed with full adders connected in serial manner. In such type of design, the output carry of one full adder is tansferred to the input carry of the next full adder. below figure shows the 3 bit binary adder which is constructed with 3 full adders.

Binary Adder/Subtractor

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

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

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

Binary Incrementer

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

Arithmetic Circuit

The basic arithmetic micro operations listed in 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 below figure.

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 full adder through the multiplexer whereas each bit of input A is connected directly to X input of full adder. The output of the circuit is calculated from the following arithmetic sum.

D = X+Y+C_in

Here X input is always equals to A input wheres Y input can be B, B, 0 or 1 according to the selection lines (S₁ and S₀) of multiplexer. C_in is the input carrry 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 below table.

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 multiplexer is B and applied to the Y input of 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 multiplexer is B and applied to the Y input of 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 output 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 two time, 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 them as binary variables. 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 below table. 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 the sixteen logic micro operations are shown in below table.

Hardware Implementation (Logic Circuit)

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

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

In the same manner, when S₁S₀=11, I₃, input will be at output of 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 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, 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 selectid bits of a register. Consider a register A which is containing the data. This operation sets the bits in register A where there are corresponding 1’s in other register B. It does not effect bit positions that have 0’s in register B. The truth table for selective set operation is given in below table.

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 previous values of register A. Therefore, the OR micro operation can be used to selective 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, which is containing the original data. This operation resets, the bits in register A where there are corresponding 0’s in other register B. It does not affect bit positions in register A that have corresponding 1’s in register B. The truth table for selective reset operation is shown in below table.

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 previous values of register A. Therefore, the AND micro operation can be used to selective 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 which is containing the data. This operation complements the bits of register A where there are corresponding 1’s in other register B. It does not make any change the bit positions that have 0’s in register B. The below table shows the truth table for selective complement opeation.

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 Ex-OR operation of bits in register B and previous values in register A. Therefore the Ex-OR micro operation can be used to selective 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 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 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. Below figure shows the 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 to the end position is to be 0 during logical shift.

Circular Shift

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

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

The above micro operation shows in figure perform arithmetic shift left to the contents of register A. This inserts a 0 into A₀, and shift all other bits to the left. If A_n-1, and A_n-2 are not same, an error may occur. In the micro operation shows in 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	The contents of register A circularly shifted left by 1-bit position. The left most bit goes into the right most bit.
A ← cir A	Circular shift right register A	Contents of register A are circularly shifted right by 1-bit position, the right most bit goes into left most bit.
A ← ashl A	Arithmetic shift left register A	Shifts 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 left most bit position.

The shift micro operations given in above table can be implemented using the circuit shown in below figure. 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 below figure.

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