FHSST Physics/Electronics/Counting Circuits

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The Free High School Science Texts: A Textbook for High School Students Studying Physics
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Electronics
Capacitive and Inductive Circuits - Filters and Signal Tuning - Active Circuit Elements - Logical Gates - Counting Circuits

Counting circuits[edit]

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[edit]

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[edit]

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[edit]