Tutorial: Wednesday Week 3

1. Tutorial: Wednesday Week 3 • Hand in on Monday, • Do the questions for tutorials 1 & 2 at the back of the course notes • (answers to tutorial 3 will be published on-line)

2. Addition & Subtraction Addition B A B A B A 2 2 1 1 0 0 C = 1 IN B A C B A C B A C IN IN IN Subtraction Full Adder Full Adder Full Adder C C C SUM SUM SUM OUT OUT OUT Q Q Q 2 1 0

3. Add / Sub Circuits Comparison • Both the addition and subtraction circuits are based around the parallel adder (using either ripple carry or carry-look-ahead). • For addition: • A and B are inputted directly to the adder • CIN = 0 • For subtraction: • A is inputted directly • All the bits of B are complemented • CIN = 1

4. ADD/SUB BIN(n) Bn 0 0 0 0 1 1 1 0 1 1 1 0 An Adder / Subtraction Circuit

5. ACTION When this signal is high, do action. ACTION When this signal is low, do action. When this signal is high, do action 1; when it’s low, do action 2. ACTION1 / ACTION2 When this signal is high, subtract; when it’s low, add. ADD / SUB Notation • To clarify a notational issue regarding the labelling of digital signals.

6. Arithmetic Logic Units • An Arithmetic Logic Unit (ALU) is a general purpose device capable of various arithmetic and logical operations. • The adder/subtractor circuit is an example of a simple ALU. • It is capable of two operations, decided by a single control input. • More elaborate ALUs are capable of numerous different operations, depending on the state of a control input word.

7. Logical Operations • As the name suggests, ALUs perform both arithmetic and logical operations. • AND, OR, XOR etc. • These operations are performed in a ‘bit-wise’ fashion. • I.e. Output bit Qn depends only on the input bits An and Bn.

8. Bitwise Logic Examples If A = 1010 and B = 1001: A AND B = 1000 A OR B = 1011 A XOR B = 0011 A NAND B = 0111 A NOR B = 0100

9. S A B X 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Logical Operations • For a single bit, imagine a logic gate that can be programmed to act either as an AND or an OR gate… X A B AND/OR Select (S)

10. Minimisation

11. 2-Bit Simple ALU AND/OR A0 B0 X0 A1 B1 X1

12. Practical ALUs • A practical ALU can perform several different operations on two multiple bit input words, A and B. • The operation is selected by a control input word, S. • Like the ADD/SUB and AND/OR circuits, the contents of all ALUs are just a big block of combinational logic. • Take, for example, the 74F382 ALU integrated circuit…

13. 74F382 • Two 4-bit input words, A and B, plus carry-in. • One 4-bit output, F, plus carry-out. • 3-bit control input word, S, eight possible permutations.

14. S2 S1 S0 Operation 0 0 0 Clear 0 0 1 B minus A 0 1 0 A minus B 0 1 1 A plus B 1 0 0 A XOR B 1 0 1 A AND B 1 1 0 A OR B 1 1 1 Set 74F382 Operations (All output bits set to zero) (bit-wise logical operations) (All output bits set to one)

15. Example Operations • (5)10 - (3)10 or (0101)2 - (0011)2 • (0101)2 XOR (0011)2

16. It’s Only Logic…

17. ALU limitations • Being just logic, ALUs require all the inputs to be present at once. • They have no memory. We’ll look at adding some next time. A B S F ALU

18. Adding Memory • Neither people or computers like having to press lots of buttons at once. • We’d both prefer a system that could remember inputs… Memory Memory A B S F ALU

19. Summary • It is reasonably straightforward to modify the adder circuit to perform either addition or subtraction (depending on a control input). • This forms a simple ALU. • Practical ALUs are capable of a wide variety of arithmetic and logical operations. • The operation is selected by a control input selection word, S. • Despite their complexity, they are only logic.