Computer ArchitectureComputer Science

Explain arithmetic microoperations.

Arithmetic Microoperations

•     Unlike register transfer microoperations, arithmetic microoperations change the information content.

• The basic arithmetic microoperations are:

  • Addition
  • Subtraction
  •  Increment
  • Decrement
  • Shift

Arithmetic Microoperations (continued)

The RTL statement:

R3 ¬ R1 + R2

indicates an add microoperation. We can similarly specify the other arithmetic microoperations.

  •  Multiplication and division are not considered microoperations.
  •  Multiplication is implemented by a sequence of adds and shifts.
  •  Division is implemented by a sequence of substracts and shifts

Binary Adder

  •  We implement a binary adder with registers to hold the data and a digital circuit to perform the addition (called a binary adder).
  • The binary adder is constructed using full adders connected in cascade so that the carry produced by one full adder becomes an input for the next.
  • Adding two n-bit numbers requires n full adders.
  • The n data bits for A and B might come from R1  and R2 respectively

Adder-Subtracter

  • Subtracting A – B is most easily done by adding B’ to A and then adding 1.
  • This makes it convenient to combine both addition and subtraction into one circuit, called an adder- subtracter.
  • M is the mode indicator
  •   M = 0 indicates addition (B is left alone and C0 is 0) M = 1 indicates

Binary Incrementer

  • The binary incrementer adds 1 to the contents of a register, e.g., a register storing 0101 would have 0110 in it after being incremented.
  • There are times when we want incrementing done independent of a register. We can accomplish this with a series of cascading half-adders.

Arithmetic Circuit

  • We can implement 7 arithmetic micro- operations (add, add with carry, subtract, subtract with borrow, increment, decrement and transfer) with one circuit.
  • We provide a series of cascading full adders with Ai and the output of a 4×1 multiplexer. 
  • The multiplexers’ inputs are two selects, Bi, Bi’,logical 0 and logical 1.
  • Which of these four values we provide (together with the carry) determines which microoperation is performed.

The Micro Operations of the Arithmetic Circuit

  • When S1S0 = 00, the MUX provides B. The result is Add (for Cin = 0) or Add With Carry (for Cin = 1).
  • When S1S0 = 01, the MUX provides B’. The result is Subtract with Borrow (for Cin = 0) or Subtract (for Cin = 1).
  •  When S1S0 = 10, the MUX provides 0. The result is Transfer (for Cin = 0) or Increment (for Cin = 1).
  • When S1S0 = 11, the MUX provides 1. The result is Decrement (for Cin = 0) or Transfer (for Cin = 1).

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