Registers and the ALU.

Step 1 of 6

Adding

A register is a small store inside the processor, close to the part that computes. This chip has two, A and B. The ALU, the arithmetic logic unit, sits between them and is always working out the sum of what they hold. The control unit decides whether the answer goes anywhere: on the execute of ADD it raises ALU out and A in, and the sum goes back into A.

First number is 100 and Second number is 50. Clock tick stands at 5: both numbers are already in the registers.

Step 2 of 6

Eight bits wrap

A register has eight bits, so it holds 0 to 255. What happens when the sum is bigger? The ALU adds bit by bit, as in column addition, with a carry passed on to the next bit. The top bit has no next bit in the register: its carry goes out to the carry flag, a small light on the ALU.

Step 3 of 6

Working out the wrap

When the ninth bit drops off, the sum loses exactly 256. So this is how to find what is left in the register: work out the true sum, and if it is 256 or more, take away 256. The lid is closed; work it out yourself.

Step 4 of 6

Subtracting

Now memory holds a different program, with SUB in place of ADD at address 2. The ALU subtracts with the same adder: it flips every bit of B, adds 1, and adds. Adding $256 - B$⁠ and then dropping 256 is exactly taking away B.

Step 5 of 6

Below zero

What if B is bigger than A? A register has no minus sign, and eight bits wrap like an odometer: one step below 0 is 255, two steps are 254. Computers that need negative numbers agree to read the numbers 128 to 255 as negative; the scheme is called two’s complement. The chip itself only wraps.

Step 6 of 6

The zero flag

Beside the carry the ALU has a second flag, zero, which lights when the last answer of an ADD or SUB is 0. A flag changes no number; it remembers something about the answer, so that a later instruction can ask about it. The two numbers here are equal.