assembly homework #1 average: 83.6234 standard deviation: 21.007 max: 100 min: 20

Assembly Homework #1

• Average: 83.6234• Standard deviation: 21.007• Max: 100• Min: 20

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

Problem #5

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 x > y x = y x < y

0 0 0 1 0

0 1 0 0 1

1 0 1 0 0

1 1 0 1 0

x > y: xy’x = y: x’y’ + xyx < y: x’y

1-bit comparator

X > Y

X = Y

X < Y

Other solutions

• More then 2 inputs for 1-bit comparator (control signal, previous results, etc)

• Using adder/substractor (note: 4-bit is not enough!)

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…

Problem #6

Z2Z1Z0 = X2X1X0 + Y2Y1Y0

X0 X1 X2

Y0 Y1 Y2 Z0

Z1

Z2

cin

cout

3-bit adder

X2 X1 X0 Y2 Y1 Y0

X0 ×Y0

X1 ×Y0

X0 ×Y2

X2 ×Y0

X1 ×Y2

X2 ×Y2

X0 ×Y1

X1 ×Y1

X2 ×Y1

3-bit adder

3-bit adder

Z1

Z0

Z2 Z3

Z4

Z5

0

0

Solution 1

half adder

x

y

s

c

full adder

x

cin

s

cout

y

full adder

full adder

half adder Z2

half adder Z3

full adder Z4

half adder

Z1

X2 X1 X0 Y2 Y1 Y0

Z5

Z0

X0 ×Y0

X0 ×Y1

X1 ×Y0

X0 ×Y2

X1 ×Y1

X2 ×Y0

X2 ×Y1

X1 ×Y2

X2 ×Y2

Solution 2

Grading policy

• 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

x2

x1

full adderx3

s

c

s

cout

cin

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

0 1 2 3 4