Assembly Homework #1

1. Assembly Homework #1 • Average: 83.6234 • Standard deviation: 21.007 • Max: 100 • Min: 20

2. Some notes • Write down your name and ID • Use A4 papers • Use standard symbols • Define your components • Do not mix circuits and logic gates • Do not plagiarize

3. Problem #5

4. Idea • X = X3X2X1X0, Y = Y3Y2Y1Y0 • X = Y: (X3=Y3)(X2=Y2)(X1=Y1)(X0=Y0) • X > Y: (X3>Y3) + (X3=Y3)(X2>Y2) + (X3=Y3)(X2=Y2) (X1>Y1) + (X3=Y3)(X2=Y2)(X1=Y1)(X0>Y0) x > y: xy’ x = y: x’y’ + xy x < y: x’y

5. 1-bit comparator

6. X > Y

7. X = Y

8. X < Y

9. Other solutions • More then 2 inputs for 1-bit comparator (control signal, previous results, etc) • Using adder/substractor (note: 4-bit is not enough!)

10. Grading policy • 5 points per each components (1-bit comparator, X>Y, X=Y, X<Y) • 15–20 points: correct with minor mistakes • 10-15 points: correct with many minor mistakes • 5-10 points: (maybe) correct major mistakes • 0-5 points: I cannot understand it…

11. Problem #6

12. Solution 1 Z2Z1Z0 = X2X1X0 + Y2Y1Y0 cin X2 X1 X0 Y2 Y1 Y0 X0 ×Y0 Y0 Y1 Y2 3-bit adder Z0 0 Z0 Z1 Z2 X1 ×Y0 3-bit adder X0 X1 X2 X2 ×Y0 Z1 X0 ×Y1 cout X1 ×Y1 0 X2 ×Y1 3-bit adder Z2 Z3 Z4 X0 ×Y2 X1 ×Y2 X2 ×Y2 Z5

13. Solution 2 X2 X1 X0 Y2 Y1 Y0 y X0 ×Y0 Z0 half adder x s X0 ×Y1 X1 ×Y0 half adder Z1 c X0 ×Y2 cin X1 ×Y1 full adder half adder Z2 x full adder X2 ×Y0 s y X2 ×Y1 full adder half adder cout Z3 X1 ×Y2 full adder Z4 X2 ×Y2 Z5

14. Grading policy x1 • No answer(-20) • No circuit drawing (-10) • Wrong circuits (-1~-5) • New component without implementation(-1~-5) • 3-to-1 multiplier (X[3..1] × Y) • Multiple-input adder (X+Y+Z) • Other error(-1~-5) half adder s x2 c cin full adder s x3 cout

15. (last digit of your ID) % 5ex: B78902011 => 1%5 = 1