Arithmetic Micro Operations

• Arithmetic micro operations are arithmetic operations such as Addition and Subtraction that are performed on the value of a register.
• The simplest form of arithmetic micro operations are increment and decrement.  
• Increment is nothing but adding value 1 to the existing content of the register.  Similarly decrement will reduce the existing value of a register by 1.
• These micro operations are imple­mented with a combinational circuit or with a binary up-down counter.

• The symbolic representation of some of the micro operations are shown in the above table along with the description
• Here is an arithmetic micro operation, which is represented using the Register Transfer Language (RTL) as follows:

                        R3 ← R1 + R2

• It specifies the add micro operation, that adds the contents of register R1 with the contents of register R2, and the sum be transferred to register R3.
• The arithmetic operations of multiply and divide are not listed in above Table. 
• These two operations are valid arithmetic operations but are not included in the basic set of micro operations.
• In most com­puters, the multiplication operation is implemented with a sequence of add and shift microoperations. 
• Division is implemented with a sequence of subtract and shift micro operations.

Implementing Micro Operation - Add:

• To implement the add microoperation with hardware, we need the registers that hold the data and the digital component that performs the arithmetic addition. 
• The digital circuit that forms the arithmetic sum of two bits and a
  previous carry is called a full-adder
• The digital circuit that generates the arithmetic sum of two binary numbers of any length is called a binary adder. 

4-bit Binary Adder

• The binary adder is constructed with full-adder circuits connected in cascade, with the output carry from one full-adder connected to the input carry of the next full-adder.
• The augend bits of A and the addend bits of B are designated by subscript numbers from right to left, with subscript 0 denoting the low-order bit. 
• The carries are connected in a chain through the full-adders. 
• The input carry to the binary adder is C0 and the output carry is C4 
• The S outputs of the full-adders generate the required sum bits.

An n-bit Binary Adder:

• An n-bit binary adder requires n full-adders. 
• The output carry from each full-adder is connected to the input carry of the next-high-order full-adder.
• The n data bits for the A inputs come from one register (such as R1), and the n data

  bits for the B inputs come from another register (such as R2).
• The sum can be transferred to a third register or to one of the source registers (R 1 or R2), replacing its previous content.

Implementing Micro Operation - Subtract:

• The Subtraction micro-operation can be done most conveniently by means
  of complements, i.e., taking the 2's complement of addend bits and adding it to the augend bits
• For example, the subtraction A - B can be done by taking the 2's complement of B and adding it to A.
• The 2's complement can be obtained by taking the 1' s complement and adding one to the least significant pair of bits. 
• The 1's complement can be implemented with inverters and a one can be added to the sum through the input carry.
• This adder-subtractor (subtraction through addition) operation can be combined into one com­mon circuit by including an exclusive-OR gate with each full-adder

4-bit adder-subtractor:

• A 4-bit adder-subtractor circuit is shown in below figure. 
• The mode input M controls the operation. When M = 0 the circuit is an adder and when M = 1 the circuit becomes a subtractor
• Each exclusive-OR gate receives input M and one of the inputs of B. 

• When M = 0, we have B ⊕ 0 = B. The full-adders receive the value of B, the input carry is O, and the circuit performs A plus B 
• When M = 1, we have B ⊕ 1 = B' and C0 = 1. The B inputs are all complemented and a 1 is added through the input carry. 
• The circuit performs the operation A plus the 2's complement of B

Binary Incrementer:

• The increment microoperation adds one to a number in a register.
• For example, if a 4-bit register has a binary value 0110, it will go to 0111 after it is incremented.

• Every time the count enable is active, the clock pulse transition increments the content of the register by one.
• The diagram of a 4-bit combinational circuit incrementer is shown in Fig. 4-8. 

• One of the inputs to the least significant half-adder (HA) is connected to logic-1 and the other input is connected to the least significant bit of the number to be incremented.
• The output carry from one half-adder is connected to one of the inputs of the next-higher-order half-adder.
• The circuit receives the four bits from A0 through A3 adds one to it, and generates the incremented output in S0 through S3. 
• The output carry C4 will be 1 only after incrementing binary 1111. This also causes outputs S0 through S1 to go to 0.