The serial binary adder or bit-serial adder is a
digital circuit In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical ...
that performs
binary
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two digits (0 and 1)
* Binary function, a function that takes two arguments
* Binary operation, a mathematical operation that t ...
addition
Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol ) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication and Division (mathematics), division. ...
bit by bit. The serial
full adder
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are ...
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
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are ...
. The flip-flop takes the carry-out signal on each clock cycle and provides its value as the carry-in signal on the next clock cycle. After all of the bits of the input operands have arrived, all of the bits of the sum have come out of the sum output.
Serial binary subtracter
The serial binary
subtracter operates the same as the serial binary adder, except the subtracted number is converted to its
two's complement
Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value (the leftmost bit in big- endian ...
before being added. Alternatively, the number to be subtracted is converted to its
ones' complement
The ones' complement of a binary number is the value obtained by inverting all the bits in the binary representation of the number (swapping 0s and 1s). The name "ones' complement" (''note this is possessive of the plural "ones", not of a sing ...
, by inverting its bits, and the carry flip-flop is initialized to a 1 instead of to 0 as in addition. The ones' complement plus the 1 is the two's complement.
Example of operation
;Decimal: 5+9=14
:*X=5, Y=9, Sum=14
;Binary: 0101+1001=1110
;Addition of each step
''*addition starts from lowest''
;Result=1110 or 14
See also
*
Parallel binary adder
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are ...
References
{{reflist
Further reading
* http://www.quinapalus.com/wires8.html
* http://www.asic-world.com/digital/arithmetic3.html
External links
Interactive Serial Adder Provides the visual logic of the Serial Adder circuit built with Teahlab's Simulator.
Binary arithmetic
Adders (electronics)