1. Arithmetic and Logic Units
Department of Communication Engineering, NCTU

2. 4.1 Serial Adder with Accumulator
Department of Communication Engineering, NCTU

3. Department of Communication Engineering, NCTU
We design a control circuit for a serial adder with an accumulator
Department of Communication Engineering, NCTU

4. Department of Communication Engineering, NCTU
Operation
Department of Communication Engineering, NCTU

5. Department of Communication Engineering, NCTU
State graph for serial adder control
Department of Communication Engineering, NCTU

6. Department of Communication Engineering, NCTU

7. Department of Communication Engineering, NCTU
4.2 A Parallel Multiplier
Department of Communication Engineering, NCTU

8. Department of Communication Engineering, NCTU
A multiplier for binary positive number
Save the product in a register
Shift the product to the right each time
Department of Communication Engineering, NCTU

9. Department of Communication Engineering, NCTU
Datapath of the multiplier
Department of Communication Engineering, NCTU

10. Department of Communication Engineering, NCTU
Operation for a simple example
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11. Department of Communication Engineering, NCTU
State graph for a straightforward implementation
Department of Communication Engineering, NCTU

12. Department of Communication Engineering, NCTU
An alternative approach
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13. Department of Communication Engineering, NCTU
Operation using a counter
Department of Communication Engineering, NCTU

14. Department of Communication Engineering, NCTU
4.3 A binary Divider
Department of Communication Engineering, NCTU

15. Department of Communication Engineering, NCTU
A parallel divider for positive numbers
A circuit to divide an 8-bit dividend by a 4-bit divisor to obtain a 5-bit quotient
Department of Communication Engineering, NCTU

16. Department of Communication Engineering, NCTU
Block diagram
Store the dividend in a register
Shift the dividend to the left each time
An extra bit is required on the left end of the dividend register
Department of Communication Engineering, NCTU

17. Department of Communication Engineering, NCTU
The operation for an example
Load initial data
Subtraction cannot be carried out without a negative result
Thus, shift the dividend to the left before we subtract
Department of Communication Engineering, NCTU

18. Department of Communication Engineering, NCTU
The quotient digit of 1 is stored in the unused position of the dividend register
Shift the dividend one place to the left
Shift once again
The first quotient digit
Department of Communication Engineering, NCTU

19. Department of Communication Engineering, NCTU
Subtraction is carried out, and the 3rd quotient digit of 1 is stored in the unused position of the dividend register
A final shift is carried out, and the 4th quotient bit is set to zero
What if the quotient is too large > 4 bits
If the initial left five bits  the divisor overflow
Department of Communication Engineering, NCTU

20. Department of Communication Engineering, NCTU
Datapath
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21. Department of Communication Engineering, NCTU
The state graph
If X8 X7 X6 X5 X4  Y3 Y2 Y1Y0  C =1  Sh and Sub and the quotient bit is 1
Otherwise  Sh and the quotient bit is 0
Department of Communication Engineering, NCTU

22. Department of Communication Engineering, NCTU
Implementation with the one-hot assignment
Department of Communication Engineering, NCTU