One Bit Adder

This web page is associated with a book called called The Animated Computer

The book can be bought at: https://play.google.com/store/books/details/Dr_Jerome_Heath_THE_EBOOK_ON_COMPUTER_DESIGN?id=WxOTBQAAQBAJ

The book gives excellent explanations for the animated images on this web site. This web page shows the animation of the computer designs in action. The book gives explanations of what the animations are about. Combining the books explanations with the animation provides a well rounded understanding of the animated computer.

Addition by Logical Gates

One method of adding two single bits from separate sources together is done using logical gates in this way

One Bit Adder

A and B are the two one bit inputs. C0 is a carry from a previous process if there is one. S is the sum. C1 is the carry to the next level of addition. Xa, Xb, and Xc define points along the route to be used in a truth table to analyze the addition circuit.

One Bit Adder Truth Table

Note: Xa, Xb, and Xc are Just locations along the process. They stand for nothing in particular. Here we are merely using those designations to keep track of the truth table processes along the way of the process.

Note: In the table Xa is A and B XOR-ed. Xb is A and B NAND-ed. Xc is C0 and Xa NAND-ed. Then S is Xa and C0 XOR-ed. And C1 is Xb and Xc NAND-ed. Also these (X) positions on the design chart have no real meaning. They are just marked places to help develop the truth table.

Note: the truth table agreement with actual addition: if A+B+C0 equals 0 then both S and C1 will to be 0; if A+B+C0 equals 1 then S needs to be 1 and C1 needs to be 0; if A+B+C0 equals 2 then S needs to be 0 and C1 needs to be 1; if A+B+C0 equals 3 then both S and C1 need to be 1.

The Animated Computer

Dr. Jerome Heath