ูตะ
ต
น ท ทองกล ม 66321695
Ch.1
วั
1. Convert these binary numbers to decimal.
(a) 10110
(b) 10001101
(c) 100100001001
(d) 01011011
2. Convert the following decimal values to binary.
(a) 37
(b) 14
(c) 189
(d) 1024
(e) 77
3. Convert each octal number to its decimal equivalent.
(a) 743
(b) 36
(c) 3777
(d) 2000
(e) 165
4. Convert each of the following decimal numbers to octal.
(a) 59
(b) 372
(c) 919
(d) 1024
(e) 771
5. Convert these hex values to decimal.
(a) 92
(b) 1A6
(c) 37FD
(d) ABCD
(e) 000F
6. Give the coded representation of the decimal number 853 in each of the following
coding schemes.
(a) 8421 code (b) 2421 code (c) Excess-3 code
(d) 2-out-of-5 code
7. What is the largest hex number that can be represented in four bytes?
8. What is the largest BCD-encoded decimal value that can be represented in three
bytes?
9. Give the coded representation for each of the following character strings as
hexadecimal numbers.
(a) 283
(b) Z = 1
(c) Bits
ช้
มี
า=
+
16 +441
=21
as,
1010 =
b)
10001101-
C).
100100001001 =+2 + + 1 =
+++1 = 128 + 8 + 4+) ==141 #
2048 + 256+ 8 + 1 = 231 *
ds. 0101011 = + 2 + + + 1 = 60 +1658++1 = 01 #
a)
37 :+29+9 = ( 100 1011,
b)
14 =
++2 = (1 1 1 0 ), #
5
7
1.
&
3
2
189 = 2 + 2 + 2 + 2 + 2 +
·
2 = (10 1/ / / 01), #
1·
d).
1024 =
2 = ( 10000000000002 #
6
e).
a)
3
2
77 = 2 + 2 + 2 +
·
2 = (1000 110) 2 #
8 + 4x8+ 3 = ( 483)
743--7.
61.36:318+ 6 - (30 )
10 #
10 #
=3x8+7x8+7x 84 = ( 2017)
C),
3777-
&1.
2000 =
2),
165:
2x8 = (1024) 10 #
1782+ 67845 = (119)
10
10
as.
59 - 1+3)
8.
7
3
372
sk &
=15648 #
5
C.
8
·We >
งาง = ( 1627) ·
#
·44 2
1
6
ds, shoe
1024 -
=18 ·
· อ
2
·
<71=
8% 3
8
PS.
(1403)
e). S41
g
(2000)
8#
Re
·
1 &
a)
853 =
1000
0101
0011 #
b)
853 =
-1110
0107
1001
C).
853:
8+3 = 11 =
10/
5+ 3 = 8 =
100
343=
853 =
d
6=
0110
1011 10000110 #
853
=1010
8
5 = 01100
01001
3=
853 =10100 01100
7),
&
01001
#
bytes = 1x8- 32bits
F = 111 7 = 15
large hex number
8).
3
bytes = 3
<8 =
in
2
bytes = ffffffff
a
bits
code
BCD = 8421
large BCD decimal = = =
24
bits =
6
group
100
of Robites
large BCD decimal in 3 bytes = 999999 *
a).
2=
b).
32
= =
1). Bits
1
=4
2 = 5A
8 =38
=69
"-" = 60
=33
283 732
7 = 7/
1 = 31
3833 #
S=
>3
"=" = 3
2 =
1 =>
51
60
3D
6031*
B Its = 22 6974 73
#
Chapter 2 and 3
1. Simplify each of the following expressions by applying one of the theorems. State the
theorem used.
(a) (ABʹ + CD)(BʹE + CD)
(b) A(C + DʹB) +Aʹ
(c) (AʹB + C + D)(AʹB + D)
(d) (A + BC) + (DE + F)(A + BC)ʹ
2. Multiply out and simplify to obtain a sum of products:
(a) (A + B)(C + B)(Dʹ + B)(ACDʹ + E)
(b) (Aʹ + B + Cʹ)(Aʹ + Cʹ + D)(Bʹ + Dʹ)
3. Factor each of the following expressions to obtain a product of sums:
(a) WX + WYʹX + ZYX
(b) ACDʹ + CʹDʹ + AʹC
4. Simplify the following expressions to a minimum sum of products. Only individual
variables should be complemented.
(a) (X + (Yʹ(Z + W)ʹ)ʹ)ʹ
(b) [(Aʹ + Bʹ)ʹ + (AʹBʹC)ʹ + CʹD]ʹ
5. Find F and G and simplify:
6. Draw a circuit that uses two OR gates and two AND gates to realize the following
function:
F = (V + W + X)(V + X + Y)(V + Z)
7. Prove algebraically:
(a) (X’ + Y’)(X ≡ Z) = (X + Y)(X Å Z) = (X Å Y) + Z’
(b) (W’ + X + Y’)(W + X’ + Y)(W + Y’ + Z) = X’Y’ + WX + XYZ + W’YZ
8. Prove the following equations using truth tables:
(a) (X + Y)(Xʹ + Z) = XZ + XʹY
(b) (X + Y)(Y + Z)(Xʹ + Z) = (X + Y)(Xʹ + Z)
a). ( AB+CD) (BE+CD/
used Distributive Laws
ABBE: B = B
=CD+
ABE #
=CD +
used Distributive
b). ALC++A
law
=CAT+ A) ( A++D
1
D#
= A++
C). CT+C+DICABHD)
used
Pistributive laws
= AB + DICAD) = /D
=AB+D #
d). +BC) + ( DE+=) ( ATBC) -
used simplification
theorems
= DETF + At+C
=At++F+DE #
as. (+AL) ( +D) ( ACD+E
(B+ACDT ( ACDTEL
ACD+BE #
NICITY
+ziX
WX+ EVX =
CN+1) +
=> CW+2) (W+) * #
⑥3.
IE+2) + BD ( +
D
+B+BBD + ADD +BDD
#
·
=- CAC+c) D+AC
=CCTC) ( +ALD+AC
= PICTHA) +AC
=CACDJLAC++A) *
=XCLEANSY
PS. CATBJCAC) ( C+D
=xvEwY
=(AABC+ABBC) ( CADT
-
=LABC) (C+P
=- XYWE #
=- ABCC+ABCD
=AB2+ ABCDE
=- ABC( ITD
=> ABC #
as. (AtB)
BTS - +#ITA
+CAT
CX+4) X = ↑
+AtBJ) = ACA+B) = OTAB
F = AB #
⑥3.
T
+
+5
CR+SJ
SI )
PTHIR+
S+
C++
↓
CR+S+TJ ( PT) /RAST + +
CRTST) IPT) ( RS) + + +
↓TT = 0
-> O+T=
&
+
CV+X+WJN+X+4) +E
N+X + WY) (V +
·
=G
E
a) = <x
+ +USITE) (
-2)
=- CUTIRE + ( +2) + COLINEXE)
=XXXZ++ XYZ + XYZ
=X + + + EVENE
=E + E CANX) + EG+)
=El + # +A ) + =( +
=· E+EXOU)
=(2) ( + <
=ETAGY) = #GUI+E #
PS. (+ ken) ( W+*+4) ( WHY+2)
า)
( +ผ แ น+WX+*** N + พ
·
·
With
XY +WE
Y twX+
เนส +win+wx +AY+
งพ =
:
(WE+Win +wX +XY+
WAYthrtW
wat
เพศ +Win+wx +AV +พ ส งห
+W A
ง = พระ+ 12 +WXZ +XYZ+WRZ
+Written +
wiz+Wi7++
+WEZtWYE+XYZ #
หั
หั
ฟั
ห์
= WX+
พั
พั
ต้
พ่
ส์
สี
ที่
พั
·
<+ 2 AtY)( AFE) <2
In
·
·
·
·
ไ
·
·
·
·
1
I
·- 1
1
/
0
/
(
=
x+ Y
·
·
·
1
·
I
·
Y
x
<2+*
·
1
0
&
0
1
1
1
1
·
0
1
·
·
·
1
0
1
1
"
&
1
·
I
1
10
/1
·
·
00
0
/
&
&
7
1
I
1
1
=
x+ Y
·
·
·
1
·
·
I
·
ไ
·
1
I
Y
x
·
·
+2 AtY) ( AFE) +E CAY) ( 2) (Y+El
·
1
0
&
0
1
1
1
1
0.1
6
1
0
1
1
1
1
10
/1
·
·
/
&
&
&
1
I
/
0
·
·
I
·
1
1
/
I
·
·
I
I
/
·
I
%