1. EEL 3705 / 3705L Digital Logic Design
Fall 2006 Instructor: Dr. Michael Frank Module #11: Signed arithmetic HW and ALUs (Thanks to Dr. Perry for some slides)
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M. Frank, EEL3705 Digital Logic, Fall 2006

2. M. Frank, EEL3705 Digital Logic, Fall 2006
Subtraction Circuit
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3. M. Frank, EEL3705 Digital Logic, Fall 2006
Subtraction Circuit
Calculate 2’s complement of B
Add –B to A
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4. M. Frank, EEL3705 Digital Logic, Fall 2006
Add/Sub Circuit
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5. Add/Sub Circuit Module
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6. Function Table for Add/Sub Module
Functional
Result
S=A+B 1
S=A-B
Add is a control input. It is active low. This means that the module will compute A+B when Add=0. It will compute A-B when Add=1.
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7. M. Frank, EEL3705 Digital Logic, Fall 2006
Add/Sub Circuit
Design using Modules
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8. M. Frank, EEL3705 Digital Logic, Fall 2006
Add/Sub Circuit
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9. M. Frank, EEL3705 Digital Logic, Fall 2006
Add/Sub Circuit
Add operation. Add=0
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10. M. Frank, EEL3705 Digital Logic, Fall 2006
Add/Sub Circuit
Sub operation. Add=1 1 1
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11. M. Frank, EEL3705 Digital Logic, Fall 2006
Comparators
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12. M. Frank, EEL3705 Digital Logic, Fall 2006
Equal Comparator
Design a logic circuit which will compute
F0 = (A = B)
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13. 2-bit Equal Comparator Truth TableF0 1
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14. 2-bit Equal Comparator Truth TableF0 1
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15. M. Frank, EEL3705 Digital Logic, Fall 2006
Solution
You can show,
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16. N-bit Equal Comparator
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17. M. Frank, EEL3705 Digital Logic, Fall 2006
Not Equal Comparator
Design a logic circuit which will compute
F = (A <> B)
F = (A = B)
i.e. Just invert our Equal Comparator circuit
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18. M. Frank, EEL3705 Digital Logic, Fall 2006
Magnitude Comparator
Design a logic circuit which will compute
F2 = (A>B)
F1 = (A<B)
Let’s develop a truth table for 2-bits
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19. 2-bit Magnitude (unsigned) Comparator Truth TableF2 F1 1
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20. 2-bit Magnitude (unsigned) Comparator Truth TableF2 F1 1
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21. M. Frank, EEL3705 Digital Logic, Fall 2006
You can show
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22. Arithmetic Logic Units (ALUs)
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23. Arithmetic Logic Unit (ALU)
A,B are data inputs of n bits each in depth
S is a control input. We have 2m operations
F is the output
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24. M. Frank, EEL3705 Digital Logic, Fall 2006
Example
Let n=4,m=3
We have A[3..0] and B[3..0]
With m=3, we have 23 = 8 operations
Let’s look at a possible function table
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25. M. Frank, EEL3705 Digital Logic, Fall 2006
Function Table s2 s1 s0
Function
F=AB 1
F=A+B (logical OR)
F=NOT A
F=A XOR B
F=A+B (Arithmetic)
F=A-B
F=A + 1
F=A - 1
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26. Design using a Truth Table
How large is the truth table?
2n from data inputs A and B
Example: n=8, we have 16 data inputs
A[7..0] and B[7..0]
3 control inputs
Total of 2n+3 inputs
N=8, we have 19 inputs
Our truth table will have
192 (361) rows and 8 outputs
Too complex. Let’s explore another alternative using a “system” or modular approach
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27. M. Frank, EEL3705 Digital Logic, Fall 2006
Design using Modules
Note:
For S2=0, we have logic operations
For S2=1, we have arithmetic operations
So, let’s use S2 to control a 2x1 MUX
to select between logic and arithmetic operations, so our top level design would look like:
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28. M. Frank, EEL3705 Digital Logic, Fall 2006
ALU Design
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29. M. Frank, EEL3705 Digital Logic, Fall 2006
ALU Design S2=0
With S2=0, F is the output from
the logic module
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30. M. Frank, EEL3705 Digital Logic, Fall 2006
ALU Design S2=1
With S2=1, F is the output from
the arithmetic module
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31. M. Frank, EEL3705 Digital Logic, Fall 2006
Logic Module Design
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32. Function Table for Logic Module
S2=0 s2 s1 s0
Function
F=AB 1
F=A+B (logical OR)
F=NOT A
F=A XOR B
We can use a 4x1 mux to
implement this module
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33. M. Frank, EEL3705 Digital Logic, Fall 2006
Logic Module Design
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34. M. Frank, EEL3705 Digital Logic, Fall 2006
Logic Module Design
F=AB
AND Operation
S[1..0]=00
0 0
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35. M. Frank, EEL3705 Digital Logic, Fall 2006
Logic Module Design
F=A+B
OR Operation
S[1..0]=01
0 1
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36. M. Frank, EEL3705 Digital Logic, Fall 2006
Logic Module Design
F=A
NOT Operation
S[1..0]=10
1 0
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37. M. Frank, EEL3705 Digital Logic, Fall 2006
Logic Module Design
F=A XOR B
XOR Operation
S[1..0]=11
1 1
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38. What do these logic modules look like?
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39. M. Frank, EEL3705 Digital Logic, Fall 2006
AND Module
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40. M. Frank, EEL3705 Digital Logic, Fall 2006
OR Module
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41. M. Frank, EEL3705 Digital Logic, Fall 2006
NOT Module A F
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42. M. Frank, EEL3705 Digital Logic, Fall 2006
XOR Module
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43. Let’s use our ADD/SUB Module
Arithmetic Module
Let’s use our ADD/SUB Module
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44. Add/Sub Circuit Module
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45. Function Table for Arithmetic Ops1
F=A+B (Arithmetic)
F=A-B
F=A + 1
F=A - 1
Note:
S0 can be use to indicate Addition or Subtraction.
S1 can be use to indicate the B data input
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46. Arithmetic Module DesignB A S
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47. Arithmetic Module DesignB A S
F=A+B
S[1..0]=00
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48. Arithmetic Module DesignB A S
F=A-B
S[1..0]=01 1
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49. Arithmetic Module DesignB A S
F=A+1
S[1..0]=10 1
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50. Arithmetic Module DesignB A S
F=A-1
S[1..0]=11 1 1
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51. M. Frank, EEL3705 Digital Logic, Fall 2006
Overall Design
We have
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52. M. Frank, EEL3705 Digital Logic, Fall 2006
ALU Design
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53. M. Frank, EEL3705 Digital Logic, Fall 2006
Logic Module Design
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54. Arithmetic Module DesignB A S
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55. M. Frank, EEL3705 Digital Logic, Fall 2006
Total Design
Logic Module
Arithmetic Module
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56. M. Frank, EEL3705 Digital Logic, Fall 2006
End of Chapter 4
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