Serial binary adder
The serial binary adder or bit-serial adder is a digital circuit that performs binary addition bit by bit. The serial full adder has three single-bit inputs for the numbers to be added and the carry in. There are two single-bit outputs for the sum and carry out. The carry-in signal is the previously calculated carry-out signal. The addition is performed by adding each bit, lowest to highest, one per clock cycle.
Serial binary addition
Serial binary addition is done by a flip-flop and a full adder as stated above. When a serial adder performs its addition, it is partially dependent on the clock cycle as a flip-flop is asynchronous and the full adder is not. Thus, when a timing diagram is done, the sum output will change as the inputs are changed, relative to the previous clock cycle which was used to determine the carry in bit. In a serial binary adder of, for example, 8 bits one bit each of data is loaded and given to the full adder during one clock cycle and the resulting sum is stored in a register. In this way the 8 bit sum is obtained after 8 clock cycles . Design is divided in two parts controller and architecture. The controller part consists of control signal like load inputs. A counter should also be used in the architecture that tells that 8 clock cycles are over and the resulting sum is obtained .
Serial binary subtracter
The serial binary subtracter operates the same as the serial binary adder, except the subtracted number is in 2's complement.
Example of operation
- Decimal
- 5+9=14
- X=5, Y=9, Sum=14
- Binary
- 0101+1001=1110
- Addition of each step
| Inputs | Outputs | |||
|---|---|---|---|---|
| Cin | X | Y | Sum | Cout |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 | 0 |
*addition starts from lowest
- Result=1110 or 14