Short Notes: Arithmetic Microoperations
Binary Adder
A digital circuit that performs arithmetic sum of binary numbers. Constructed with full-adders
connected in cascade. Each FA generates sum and carry, with carry output connected to next FA.
An n-bit adder requires n full-adders. Used for register-to-register addition.
Binary Adder-Subtractor
Performs subtraction A - B by taking 2’s complement of B and adding it to A. The 2’s complement is
obtained by inverting bits of B and adding 1. A control input determines whether operation is
addition (M=0) or subtraction (M=1).
Binary Incrementer
Used to increase a number in a register by 1. Constructed with half-adders connected in cascade.
The LSB input is tied to logic-1, and the carry propagates through half-adders. Output increments
binary value by 1 each cycle.
Arithmetic Circuit
Implements arithmetic microoperations (add, subtract, increment, etc.) using multiplexers and
full-adders. Has inputs A and B, multiplexers select between B, ~B, or 0. Control signals S2, S1, S0
select the operation. Output equation: D = A + Y + Cin, where Y depends on selected operation.
Functions of Arithmetic Circuit
Seven microoperations: 1. Add (A + B) 2. Add with carry (A + B + 1) 3. Subtract with borrow (A + B'
+ 1) 4. Subtract (A + B') 5. Increment A (A + 1) 6. Decrement A (A - 1) 7. Transfer A (output = A).