1. Computer Architecture and Organization: L05: Arithmetic Micro-operations
By: A. H. Abdul Hafez
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

2. Outlines Arithmetic microoperation Full adder Four bit parallel adder
Adder – subtractor circuit
Four bits arithmetic circuit
One stage logic unite
Logic microoperation example
Shift microoperation
Logic shift
Circular shift
Arithmetic shift
Shift unit
ALU
End
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

3. Main Types of Microoperations in Digital Computers
Register Transfer Microoperations transfer binary information from one register to another.
Arithmetic Microoperations perform arithmetic operations on numeric data stored in registers.
Logic Microoperations perform bit manipulation operations on (non-numeric) data stored in registers.
Shift Microoperations perform shift operations on data stored in registers.
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

4. Arithmetic Microoperations
Symbolic Designation
Description
R3  R1 + R2
Contents of R1 plus R2 transferred to R3
R3  R1 – R2
Contents of R1 minus R2 transferred to R3
R2  R’2
Complement of the contents of R2 (1’s complement)
R2  R’2 + 1
2’s complement of the contents of R2
R3  R1 + R’2 + 1
R1 plus the 2’s complement of R2 (subtraction)
R1  R1 + 1
Increment the contents of R1 by one
R1  R1 -1
Decrement the contents of R1 by one
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

5. The full Adder Half Adder 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 x y c s x y
x y c s x y c s
c = xy s = xy’ + x’y
= x  y
Full Adder
x y cn cn s x y S cn
cn-1
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

6. The full Adder
The full adder accepts two input bits and an input carry and generates a sum output and an output carry A B
Cin
Cout ∑ 1
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

7. Four-bits parallel adder
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

8. 2’s complement form
A negative value is the 2’s complement of the corresponding positive value.
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

9. Binary adder-subtractor
M=0  Add
M=1  Subtract M C4 C3 C2 C1 C0 FA FA FA FA S3 S2 S1 S0
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

10. 4-bit Arithmetic Circuit
Cin A0 FA C0
4-bit Arithmetic Circuit X0 S1 S1
4x1
MUX S0 S0 D0 B0 Y0 C1 1 2 1 3 A1 X1 FA S1
4x1
MUX S0 D1 B1 Y1 C2 1 2 1 3
The output of the circuit is represented by the expression:
D= A + Y + Cin A2 X2 FA S1
4x1
MUX S0 D2 B2 Y2 C3 1 2
The value of Y is depend on the value of the selector lines. 1 3 A3 X3 FA S1
4x1
MUX S0 D3 B3 Y3 1 C4
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU 2
January 10, 2019 1 3
Cout

11. Arithmetic Circuit Function Table
Select
Input
Output
Microoperation S1 S0
Cin Y
D = A + Y + Cin B
D = A + B
Add 1
D = A + B + 1
Add with carry B’
Subtract with borrow
Subtract
D = A
Transfer A
D = A + 1
Increment A
D = A - 1
Decrement A
Arithmetic Circuit Function Table
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

12. Logic Microoperations
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

13. One Stage Logic Circuit
4x1
MUX S0 Ai Bi Ei 1 S1 S0
Output
Operation
E = A  B
AND 1
E = A  B OR
E = A  B
XOR
E = A
Complement 2 3

14. Logic microoperation Examples
Selective set
Selective clear
Selective complement
Mask
Compare
Insert
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

15. A or B Selective Set 1010 Content of Register A before Microoperation
Setting a bit is turning that bit on (making it 1)
0  1
1  1
1010 Content of Register A before Microoperation
1100 Content of Register B (Logic Operand)
1110 Content of Register A after Microoperation
What is the logic function that performs the selective set micro-operation ?
A or B

16. Selective Clear 1010 A Before 1100 B (Logic Operand) -------
Clearing a bit is turning that bit off (making it 0)
0  0
1  0
A Before
B (Logic Operand)
A after
What is the logic function that performs the selective clear micro-operation ?
A and B

17. Selective Complement 1010 A Before 1100 B (Logic Operand) -------
Complementing a bit is negating the bit
0  1
1  0
1010 A Before
1100 B (Logic Operand)
0110 A after
What is the logic function that performs the selective complement micro-operation ?
A xor B

18. Mask (Select) Operation
Masking a bit is selecting the bit if the mask bit is 1
Mask bit = 1  0  0 , 1  1
Mask bit = 0 1  0 , 0  0
1010 A Before
1100 B (Mask)
1000 A after
What is the logic function that performs the mask micro-operation ?
A and B

19. Compare Microoperation
A  A  B
1010 A
1010 B
0000 A  A  B

20. Insert Microoperation
Inserting a group of bits into one part of a register
e.g. insert 1001 into the most significant nibble of a register
A Before
B (mask)
A after
Microoperation 1
Step no.1 Masking
(A And B)
A Before
B (insert)
A after
Step No.2
(A OR B)
Microoperation 2

21. Shift microoperations
Logical shift : transfers 0 through the serial input 7
Logical Shift
R2← shr R2
R1← shl R1
Circular shift : circulates the bits around the two ends without loss the information. 7
R1← cil R1
R2← cir R2 7
Circular Shift (Rotate)
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

22. Shift microoperations
Arithmetic shift: shifts a signed binary number to the left or to the right. The sign bit must not changed because the sign of the number remains the same. 7
Arithmetic Shift Right (Divide by 2)
R← ashr R -8 4 2 1 -8 4 2 1
Before 1 1
Before 1 1 1 1
After 1 1 1
After
Negative Numbers
Positive Numbers
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019
Negative Numbers
Positive Numbers

23. Shift microoperations
Arithmetic shift: shifts a signed binary number to the left or to the right. The sign bit may be changed. 7
Arithmetic Shift Left (Multiply by 2)
R← ashl R -8 4 2 1 -8 4 2 1
Before 1
Before 1 1 1
After 1 1
After
No Overflow
Overflow !
Overflow occurs if, before the shift, Vs = Rn-1  Rn-2
Vs = R3  R2
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

24. 4-bits combinational circuit shifter
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

25. Arithmetic logic shift unit ALU
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

26. Function Table for Arithmetic Logic Shift Unit
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019

27. The end of the Lecture Thanks for your time Questions are welcome
CAO, by Dr. A.H. Abdul Hafez, CE Dept. HKU
January 10, 2019