2. EE365 Adv. Digital Circuit Design Clarkson University Lecture #9 Math Units ROMs

3. Topics Comparators Adders Multipliers ROMs Rissacher EE365Lect #9

4. Equality Comparators 1-bit comparator 4-bit comparator EQ_L Rissacher EE365Lect #9

5. 8-bit Magnitude Comparator Rissacher EE365Lect #9

6. Other conditions Rissacher EE365Lect #9

7. 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 Rissacher EE365Lect #9

8. Full-adder circuit Rissacher EE365Lect #9

9. 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 look-ahead Rissacher EE365Lect #9

10. 74x283 4-bit adder Uses carry look-ahead internally Rissacher EE365Lect #9

11. “generate” “propagate” “half sum” carry-in from previous stage Rissacher EE365Lect #9

12. Ripple carry between groups Rissacher EE365Lect #9

13. Look-ahead carry between groups Rissacher EE365Lect #9

14. 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. Subtraction Rissacher EE365Lect #9

15. Full subtractor = full adder, almost Rissacher EE365Lect #9

16. Multipliers 8x8 multiplier Rissacher EE365Lect #9

17. Full-adder array Rissacher EE365Lect #9

18. Faster carry chain Rissacher EE365Lect #9

19. Read-Only Memories Rissacher EE365Lect #9

20. 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 Rissacher EE365Lect #9

21. Logic-in- ROM example Rissacher EE365Lect #9

22. 4x4 multiplier example Rissacher EE365Lect #9

23. Internal ROM structure PDP-11 boot ROM (64 words, 1024 diodes) Rissacher EE365Lect #9

24. Two-dimensional decoding ? Rissacher EE365Lect #9

25. Larger example, 32Kx8 ROM Rissacher EE365Lect #9

26. Today’s ROMs 256K bytes, 1M byte, or larger Use MOS transistors Rissacher EE365Lect #9

27. EEPROMs, Flash PROMs Programmable and erasable using floating-gate MOS transistors Rissacher EE365Lect #9

28. Typical commercial EEPROMs Rissacher EE365Lect #9

29. 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) Rissacher EE365Lect #9

30. Microprocessor EPROM application Rissacher EE365Lect #9

31. ROM control and I/O signals Rissacher EE365Lect #9

32. Next time Latches Flip Flops Clocking Rissacher EE365Lect #9