A full adder and the processor.

Step 1 of 5

A full adder

A full adder adds three bits: $a$⁠, $b$⁠, and a carry in from the column to its right. Their sum is between $0$⁠ and $3$⁠, so it always fits in two bits: a sum digit and a carry out. It is built from two half adders: the first adds $a$⁠ and $b$⁠, the second adds the carry in to the result, and an OR gate joins the two carries.

This is a toy eight-bit processor. Its program adds the First number and the Second number, $28 + 14$⁠, and it is now decoding the add instruction. Predict, and then Zoom into the chip will raise a loupe over bit 3 of the arithmetic unit, one full adder, transistor by transistor.

Step 2 of 5

Column addition

Binary addition is the same column addition as at school, only with two digits: from right to left, column by column, and whenever a column reaches 2, write the sum digit and carry 1 to the left. Here is $28 + 14$⁠:

$\begin{array}{r} 0001\,1100 \\ +\ 0000\,1110 \\ \hline \end{array}$⁠

Fill in the bottom row.

Step 3 of 5

Eight adders

The arithmetic unit, the ALU, is eight full adders in a row, one per bit. The carry out of each is the carry in of the one to its left. The loupe shows one of them: a CMOS full adder is 28 transistors, and a real processor holds millions of copies of circuits like it.

Step 4 of 5

Overflow

Eight adders hold eight bits, so a result over 255 does not fit. The carry out of the leftmost bit is not lost: the processor keeps it in the carry flag, which a program can test. The numbers here are $200$⁠ and $100$⁠. Move Clock tick to run the program, and see what is stored in cell 13.

Step 5 of 5

A byte in memory

The processor’s memory shows each cell as eight bits. The First number is stored in cell 14, and the second in cell 15. When you change the number, you write a new byte into memory.