CPE 223 Digital Electronics and Logic Design

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1. Use 16-bit 2's complement binary to represent the following decimal numbers: (3 points) a) 14,320

b) -12,035

c) 0.12

2

(3)

2. Perform binary additions or subtractions and determine whether the overflow occurs.

a) 1001 1011

+

10110110

c) 1000 0001 1011 0110

b) 0110 1010 10101111

d) 0110 1010 + 0100 0101

(2 points)

(4)

3. Simplify the following Boolean functions:

a) F(A,B,C,D)

=

^1:(0,l,4,5,12,13)

b) F(W,X,Y,Z) = I: (1,7,11,13) + d(0,5,10,15)

c) F(A,B, C,D) =ABC+ BCD+ ACD

+

ABD

(3 points)

4

(5)

4. Given the following function in sum of products form F(A,B,C,D) =ABC+ AD+ AC

a)

Determine F in minimized sum of products form.

b)

Implement Fusing NAND gates only.

(4 points)

(6)

5. Implement the following Boolean function using two 4-to-1 multiplexers. (4 points) F(A,B,C,D)

=

^:E(2,4,6,9,10,11,15)

E

Do _II

Di _4-fo.1 1'l ^MUX DJ

It

E Do

D1 4-to-l D2 ^MUX

~

Io It

6

(7)

6. A combinational circuit is specified by the following three Boolean functions:

F1(A,B,C)

=

l: (0,3,4) F2(A,B,C)

=

^L^{(1,2, 7)}

FJ(A,B,C) == TI (0, 1,2,4)

1mp1ement the circuit with two 2-to-4 decoders.

I

4

B l-to-4 f1

- G 4ec:oc1er· ~

f3

4 Yo

B l-to-4 Y1 G dcood« Y2 f3

(4 points)

(8)

7. Given the circuit shown below(Assume flip-flops are initially in reset state): (6 points)

x _ _ ....,. D Q --- .---D Q y

Q ~---

Clk - - - ~

a) Determine the output (y) waveform

X

Clk

y ---

b) Sketch the state diagram

8

(9)

8. Given the circuit below(Similar to the one in the Laboratory section):

CLK INIT=LOW START=O COUNT=-1 CLOCK=256

JUl

~

r+

U2

•CKA QA

CKB QB

QC OD R0(1)

R0(2) 7493U

4

ANO

[D© -- - -

-+

_R

11

3

-

1R . .,,,

-- - -

U3

1 A YO ¹⁵

? t.t

3 B Y1

C Y2 13 Y3 17

11

.t Y4

t±

s:: ^E1 ^Y5

6 E2 Y6

E3 Y7

74HC238

U1

N) 00 ^!

A1 01

A2. D2

A3 D3

A,4 D4

A5 05 15

N; 06 16

~

A7 07

NJ A9 A10 A11

CE OE/VPP 2732

Specify the ROM contents so that the dot-matrix displays the letter "B" as shown:

Address ROM contents (in binarv) (in binarv)

0000 0001

RowO

" II 0-..,

Row1

eoooe

Row2

eoooe

Row3

••••o

Row4

roooe

Row5

•oooe

Row6 I 0

RowEi

KOW(

(4 points)

(10)

Supplemental Table 2.1

Postulates and Theorems of Boolean Algebra

Postulate 2 (a) x+O=x

Postulate 5 (a) X + x'

=

1

Theorem l (a) X + ^X

=

^X

Theorem 2 (a) X + 1

= }

Theorem 3. involution (x')'

=

^X

Postulate 3. commutative (a) x+y=y+x Theorem 4. associative (a) X + (y + Z)

=

^(X+ J') + .::

(b) x-1 =x

(b) x·x' =O (b) x·x =x (b) x ·O = 0

(b) xy

=

^yx

(b) x(yz)

=

^(xy)z

Postulate 4. distributive (a) x(y+.::)=xy+xz (b) x + y.::

=

^(x⁺^y)(x^{+ .::)}

Theorem 5. DeMorgan (a) (x + y)'

=

^x'y' ^(b) ^(xy)'

=

^x'⁺^y'

Theorem 6. absorption (a) X + xy

=

^X ^(b) ^x(x⁺^y)

=

^x

Table 5.1

Flip-Flop Characteristic Tables

JK Flip-Flop

I K Q(t + 1)

0 0 Q(I) No change

0 1

⁽⁾

Reset

l 0 l Set

I l Q'(t) Complement

D Fllp-Flop T Fllp-Flop

D Q(t + 1) T Q(t + 1)

0 0 Reset 0 Q(l) No change

'-·

1 1 Set 1 Q'(f) Complement

10