2. 1 EE 365 Adders Multipliers Read-Only Memories

3. 2 Equality Comparators 1-bit comparator 4-bit comparator EQ_L

4. 3 8-bit Magnitude Comparator

5. 4 Other conditions

6. 5 Adders Basic building block is “full adder” –1-bit-wide adder, produces sum and carry outputs Truth table: XYCinSCout 00000 00110 01010 01101 10010 10101 11001 11111

7. 6 Full-adder circuit

8. 7 Ripple adder Speed limited by carry chain Faster adders eliminate or limit carry chain –2-level AND-OR logic ==> 2 n product terms –3 or 4 levels of logic, carry lookahead

9. 8 74x283 4-bit adder Uses carry lookahead internally

10. 9 “generate” “propagate” “half sum” carry-in from previous stage

11. 10 Ripple carry between groups

12. 11 Lookahead carry between groups

13. 12 Subtraction Subtraction is the same as addition of the two’s complement. The two’s complement is the bit-by-bit complement plus 1. Therefore, X – Y = X + Y + 1. –Complement Y inputs to adder, set C in to 1. –For a borrow, set C in to 0.

14. 13 Full subtractor = full adder, almost

15. 14 Multipliers 8x8 multiplier

16. 15 Full-adder array

17. 16 Faster carry chain

18. 17 Read-Only Memories

19. 18 Why “ROM”? Program storage –Boot ROM for personal computers –Complete application storage for embedded systems. Actually, a ROM is a combinational circuit, basically a truth-table lookup. –Can perform any combinational logic function –Address inputs = function inputs –Data outputs = function outputs

20. 19 Logic-in-ROM example

21. 20 4x4 multiplier example

22. 21 Internal ROM structure PDP-11 boot ROM (64 words, 1024 diodes)

23. 22 Two-dimensional decoding ?

24. 23 Larger example, 32Kx8 ROM

25. 24 Today’s ROMs 256K bytes, 1M byte, or larger Use MOS transistors

26. 25 EEPROMs, Flash PROMs Programmable and erasable using floating-gate MOS transistors

27. 26 Typical commercial EEPROMs

28. 27 EEPROM programming Apply a higher voltage to force bit change –E.g., VPP = 12 V –On-chip high-voltage “charge pump” in newer chips Erase bits –Byte-byte –Entire chip (“flash”) –One block (typically 32K - 66K bytes) at a time Programming and erasing are a lot slower than reading (milliseconds vs. 10’s of nanoseconds)

29. 28 Microprocessor EPROM application

30. 29 ROM control and I/O signals

31. 30 ROM timing