How Does an ALU Work?

Try this book 8051 microcontroller -Ayala

If I remember correctly from my microcoding days back in college (too many years ago), a comparison like that is done by doing a subtraction (do the appropriate complement of one of the numbers and add), then look at the overflow. If the difference takes you into the negative, you subtracted the larger from the smaller. You can do a test for "equals" by doing an "exclusive or" of the two numbers and testing for the result being zero.

Most of the arithmetic operations are based on basic logic operations (invert, and, or, xor), shift, and addition.

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PeterT,

Thanks for the explanation for the </> part. I think I got the addition part understood. What I"m really looking for is a diagram/schematic for the internal ALU. I've found a few sites now that show the inputs output wiring schematic, but I'm really curious about the actual ALU hard wiring. Haven't found any sites showing that level of detail

This is quite a curious question. Why do you need to know how it works? Years ago electronics courses used to teach this, but today it is not required knowledge, as ALU operations are effectively transparent, due to how code-writing utilities have advanced.

Where/how will you use this knowledge?

Look up a binary adder on the web. When two or more logical adders are cascaded, one can add multi-bit binary numbers. By using two's complement, one can also subtract. With a little creativity and a fair amount of logic, one can multiply and divide. The whole subject actually a good chunk of the curriculum for a course on microprocessors.

Typical ALU's have binary inputs for the variables and some control inputs to select the arithmetic function. Floating Point Processors are all the more complicated. Note that before 486's and Pentium's, the FPU was a separate chip when used with the 80286 and 80386, the predecessors of today's PC processors.

Wikipedia has some very good info on them as well.

Wikipedia is good for this sort of thing; start here:-

http://en.wikipedia.org/wiki/Adder_(electronics)

Also here:-

http://en.wikipedia.org/wiki/Arithmetic_logic_unit

An ALU is just a bunch of digital logic gates hardwired to work in parallel to maximize speed. The logic functions that the ALU performs varies by application.

Comparing the values of two numbers such as your 2 & 4 requires a circuit called a digital magnitude comparator. The power point tutorial in the below link should provide the answer that you seek.

ece.gmu.edu/~clorie/Spring10/ECE-301/Lectures/Lecture_11.ppt

Well to answer the how of the "mechanical" part...it's basically a bunch of relays which are wired to be AND, OR, and XOR gates. Of course today they use transistors/ICs rather than mechanical relays.

When I was in high school I helped a friend of mine build a computer that used only relays, and a few tubes, and did only one task.