1. Computer Science 210Computer Organization The Arithmetic Logic Unit

2. ALU - General • Goal is to design simple ALU • Actually there are relatively few basic arithmetic logic operations needed • Many instructions can be implemented in terms of the basic ones

3. AND Gate Multiplexor NOT Gate ALU Building Blocks OR Gate

4. operation a result b An ALU (arithmetic logic unit) • Let's build an ALU to support the andi and ori instructions • we'll just build a 1 bit ALU, and use 32 of them

5. Review: The Multiplexer • Selects one of the inputs to be the output, based on a control input • We’ll use a MUX for our ALU S 01 A C B

6. 1-Bit Logical Unit Operation Result 01 0 - AndOperation 1 - Or

7. 1-Bit ALU with Addition O p e r a t i o n C a r r y I n a 0 1 R e s u l t 2 b C a r r y O u t

8. 32 bit ALU

9. What about subtraction (a – b) ? • Two's complement approach: just negate b and add one. • How do we negate?

10. 32 bit ALU binvert binvert O p e r a t i o n C a r r y I n a 0 1 R e s u l t + 0 b 2 1 C a r r y O u t binvert = 1, carryin = 1, operation = 2, gives a + ~b + 1 = a - b

11. Overflow Detection Note: This can be determined by what happens in the high order bit.

12. Overflow Detection Note: If we used the output of the binvert MUX, the rows for subtraction would be the same as for addition.

13. Overflow Detection Note: The other rows of a truth table for Overflow would be 0. So, we could build an overflow detector with _ _ _ AMR + AMR

14. High Order 1-Bit ALU(with overflow hardware) B i n v e r t O p e r a t i o n C a r r y I n a 0 1 R e s u l t 0 b 2 1 Overflow C a r r y O u t