1. EE121 John Wakerly Lecture #6
Adders
Multipliers
Read-Only Memories
Barrel-Shifter Design Example

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

3. 8-bit Magnitude Comparator

4. Other conditions

5. Comparators in ABEL Equality checking PEQQ = ([P7..P0] == [Q7..Q0]);
PEQQ_L = !([P7..P0] == [Q7..Q0]);
16 product terms
Magnitude comparison
PGTQ = ([P7..P0] > [Q7..Q0]);
PGTQ_L = !([P7..P0] > [Q7..Q0]);
255 product terms (try it in Foundation!)

6. Adders Basic building block is “full adder” Truth table:
1-bit-wide adder, produces sum and carry outputs
Truth table:
X Y Cin S Cout

7. Full-adder circuit

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

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

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

11. Ripple carry between groups

12. Lookahead carry between groups

13. Addition in ABEL Easy? No -- huge number of product terms!
On the order of 2n for bit n
@CARRY directive

14. 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 Cin to 1.
For a borrow, set Cin to 0.

15. Full subtractor = full adder, almost

16. Multipliers
8x8 multiplier

17. 4x4 multiplier in ABEL

18. Full-adder array

19. Faster carry chain

20. Read-Only Memories

21. 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

22. Logic-in-ROM example

23. 4x4 multiplier example

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

25. Two-dimensional decoding?

26. Larger example, 32Kx8 ROM

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

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

29. Typical commercial EEPROMs

30. 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)

31. Microprocessor EPROM application

32. ROM control and I/O signals

33. ROM timing

34. Next time
Sequential circuits (Chapter 7)