FHSST Physics/Electronics/Counting Circuits

Counting circuits An arithmetic and logical unit (ALU) adder provides the basic functionality of arithmetic operations within a computer, and is a significant component of the arithmetic and logical unit. Adders are composed of half adders and full adders, which add two-bit binary pairs, and ripple carry adders and carry look ahead adders which do addition operations to a series of binary numbers. Note: Pictures on wikipedia under GFDL Half Adder A half adder is a logical circuit that performs an addition operation on two binary digits. The half adder produces a sum and a carry value which are both binary digits. Sum(s) = A xor B Cot(c) = A and B Following is the logic table for a half adder: A B Sum Cot 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 Half adder circuit diagram Full adder A full adder is a logical circuit that performs an addition operation on three binary digits. The full adder produces a sum and carry value, which are both binary digits. Sum = (A xor B) xor Cin Cot = (A nand B) nand (Cin nand (A xor B)) A B Cin Sum Cot 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 Full adder circuit diagram References Microprocessor Design/Add and Subtract Blocks Microprocessor Design/ALU Electronics/ALU