-
8/10/2019 Chapter 01 Suggested Solution
1/19
2010 Chung Tai Educational Press. All rights reserved.
Worksheet 1A(page 1.1)1. (a)
2
222
4
2)2(
a
aa
=
=
(b)63
6332)(
ba
baab
=
=
2. (a)
3
6
3
633
2
64
4)
4(
q
p
q
p
q
p
=
=
(b)
6
2
62
222
3
4
2
)1()
2(
q
p
q
p
q
p
=
=
3. (a)3
32
12
12)4)(3(
a
aaa
=
=
(b)
b
a
b
ba
b
abab
2
4
32
4
2))((
=
=
4. (a)
4
22
2
14
7
4
3
32
3
ba
aab
aa
ba
=
=
(b )
y
x
x
y
y
x
x
y
y
x
x
yx
y
xy
=
=
=
)4
(2
)4
()2()
4()
2(
22
2
2
3
22
2
5. (a)
2
2
2
4
22
1212
=
=
++
n
n
n
n
(b )
22
2
3
2
3
3
3
3
27
++
=
=
n
n
n
n
n
6. (a)
3
2
2)14(
2
222
2
22 22
=
=
=
+
n
n
n
nn
n
nn
(b )
4
10
!
3)1"(
3)1"(
333
333
33
332
2
2
2
=
=
+
=
+
=
+
+
+
n
n
nn
nn
nn
nn
Worksheet 1B(page 1.3)
1. (a)
2
1
1
2
2
=
=
(b )1
1)"( 440
=
=
1
-
8/10/2019 Chapter 01 Suggested Solution
2/19
2010 Chung Tai Educational Press. All rights reserved.
(c)
"
2
1
1)(
1)
3
2()
3(
2
"
2
3
02
=
=
=
2. (a)
32
1
a
aaa
=
=
(b)
b
a
baba
3
3)3(
2
12112
=
=
3. (a)a
bababa
4
4)4)((
01112
=
=
(b)!24
!3243 )(#)$(
ba
baba
=
=
4. (a)
4
41
22
21
21
12
)(
)(
b
a
ba
ba
ba
ba
ab
=
=
=
(b)
4
4
44
2
!4
422
42
2
"
3
1
3)
3(
b
a
ba
ba
b
ba
b
=
=
=
5. (a)
10
6
106
2
6642322220
16
4
1
4)()4(
b
a
ba
babbaba
=
=
=
(b)
4
4
44
2
3
41026322302
16
12
4
4)4()(
b
a
ba
baababa
=
=
=
(c )
"7
4
"74
3
2
62223"63
231332
27
16
3
4
43
)4()3(
cb
a
cba
cbacba
bcacba
=
=
=
(d)
"
7
7"
1
3
131
66313322
24
3
23
2)3()2(
a
b
ba
ba
bababa
=
=
=
Worksheet 1C(page 1.5)1. (a)
6
1034.2
000000134.20003402
=
=
(b)3104.2
001.04.24002.0
=
=
2. (a)210472.1
100472.12.147
=
=
(b)6102.1
001000.02.12001000.0
=
=
3. (a)
!
102
1010
10001.3
1010001.3
10100001.3101.300
=
=
=
(b)
12
164
1616
103."
10103."
101000.03."10"3000.0
=
=
=
4. (a)
2
-
8/10/2019 Chapter 01 Suggested Solution
3/19
2010 Chung Tai Educational Press. All rights reserved.
7
43
44
10.4
1010.4
10001.0.410004.0
=
=
=
(b)
1
20
2020
10.1
1010.1
10000100.11000010
=
=
=
5. (a)10
"16
107!1.1
10!1.17)10()1062.3(
=
=
(b)
13
12
!
4
1022.2
10222.010!
10776.1
=
=
6. (a)4
10!276.3
76!32!
=
=
!
102"06.3
623"0
=
=
( b ) % r o & ( a ) ' ! i s l a r g e r .
Worksheet 1D(page 1.7)1. (a)
2
01234
3
101011
212120212021
1212121
=
+++++=
+++
(b)
2
01234
1234
11110
2021212121
21212121
2141!1161
=
++++=
+++=
+++
2. (a) 0122 212021101 ++=
(b)01234
2 212121202110111 ++++=
3. (a)
27
12!16
2222
212120212111011
0134
012342
=
+++=
+++=
++++=
(b )
2"
14!16
2222
212021212111101
0234
012342
=
+++=
+++=
++++=
4. (a)
2
41632
222
202021202121
110100
24
01234
2
=
++=
++=
+++++=
(b )
37
1432
222
212021202021
100101
02
01234
2
=
++=
++=
+++++=
5. (a) ivide 22 * 2 continuousl*' +e get
0
, e & a i n d e r
1
1
0
112
222
2
22
1 21011022 =
(b ) ivide 26 * 2 continuousl*' +e get
0
, e & a i n d e r
1
0
1
132
262
62
32
1
3
-
8/10/2019 Chapter 01 Suggested Solution
4/19
2010 Chung Tai Educational Press. All rights reserved.
21101026 =
(c) ivide 121 * 2 continuousl*' +e get
1
, e & a i n d e r
0
0
1
1
602
1212
302
12
72
3
11
2
21111001121 =
(d) ivide 1"" * 2 continuousl*' +e get
1
, e & a i n d e r
1
1
0
0
""2
1""2
4"2
242
122
6
0
1
32
1
2
2110001111"" =
Worksheet 1E(page 1.9)1. (a)
16
01234
124
0E10
160161416160161
161416161
=
++++=
++
(b)
16
012
34
034
001A-A
161160160
161016111610
161161016111610
=
+++
++=
+++
2. (a) 0116 16111611-- +=
(b) 01216 16141601613E0 ++=
3. (a)
1"
3161
1631611301
16
=
+=
+=
(b)
0774
131614261
16131614161%E
01216
=
++=
++=
(c )
"6
121611263
16121611163-C3 01216
=
++=
++=
(d)
10"4
13000"641
1613160160161100
012316
=
+++=
+++=
4. (a) ivide 1" * 16 continuousl*' +e get
3
, e & a i n d e r
1
1"16
16
131" =
(b) ivide 13! * 16 continuousl*' +e get
10(A)!
13!16 , e & a i n d e r
16A!13! =
(c ) ivide 401 * 16 continuousl*' +e get
1
, e & a i n d e r
"216
40116
1
161"1401 =
(d) ivide 1 67! * 16 continuous l*' +e get
14(E)
, e & a i n d e r
3
13()
"7"16
1 67!16
6116
3
4
-
8/10/2019 Chapter 01 Suggested Solution
5/19
2010 Chung Tai Educational Press. All rights reserved.
16E3367!1 =
Build-up Exercise 1A(page 1.11)1. (a)
7
14242
a
aaaa
=
= ++
(b)
42
1311
33
!
!
)2(4)2)(4(
ba
ba
bbaaabab
=
=
=
++
(c)
3
33
3
36
3
6
b
b
b
b
=
=
2. (a)3
333
27
3)3(
x
xx
=
=
(b)101
2323
32
2)1()2(
yx
yxyx
=
=
(c)61
32332
3
3)(3
yx
yxyx
=
=
3. (a)
2
22
2
22
4
"
2
"
)(2
3)
2
3(
h
h
hh
=
=
=
(b)
4
6
4
232
22
232
2
3
4
2
)2()
2(
k
h
k
h
k
h
k
h
=
=
=
(c )
3
6
33
323
3
323
2
12
!
2
)(
)2()
2(
h
k
h
k
h
k
h
k
=
=
=
4. (a)
2
1012
12
10
12
64
12
64
1
1
))((
p
p
p
p
p
p
p
pp
=
=
=
=
+
(b )
3
4
2
4
2424
!
!
3
243)24(
q
p
q
p
q
qpqqp
=
=
=
(c )
24
1113
33
10
10
2))(2)((
qp
qp
qqpppqqp
=
=
=
++
5. (a)7
24333223
)1()()(
ba
bababaab
=
=
(b )
110
31264
36312443243
432
2716
32)3()2(
ba
bbaa
bababaab
=
=
=
6. (a)
"
)3(
)3
()6
2(
42
2
42
22
2
2
33
yx
yx
xy
yx
yx
=
=
=
5
-
8/10/2019 Chapter 01 Suggested Solution
6/19
2010 Chung Tai Educational Press. All rights reserved.
(b)
2
"
2
32
)2
3(2)
6
"(2
2
2
22
22
2
3
y
y
y
xy
xy
=
=
=
7. (a)
6
2
3
2
24
22
2
2
4
2
1
)1
(
)()()(
y
y
x
y
y
x
x
y
y
x
=
=
=
(b)
3
3
"
4
"
3
4
"
33
4
3
3
2
2
!
!
1
!1
21)
2()
1(
x
y
x
y
y
y
x
y
y
x
yy
x
y
=
=
=
=
8. (a)
v
u
vu
vu
vu
vu
uv
vu
16
64
4
4
2
)4(
)2(
33
24
333
224
3
22
=
=
=
(b)
2
44
6
442
6332
222
322
2
4
!
2
2
)2(
)2)((
uv
vu
vu
vu
vuu
vu
uvu
=
=
=
9. (a)
q
p
qp
qp
qp
qpqppq
qp
qpqppq
74
6"
74
46222
74
232
1!
1!
1!
)3)(2)((
1!
)3)(2)((
=
=
=
(b)
q
p
qp
qp
qp
qqpp
pq
qqpp
7
62
"
622
33242
23
322
4
36
144
6
)2)(3)(2(
)6(
)2()3)(2(
=
=
=
10. (a)
"
7
326
"
34
23
2
3
)1
)(()()(
n
m
nmn
m
nm
m
n
m
=
=
(b)
4
2
4
!
6
!
4
6
!4
44
63
3
4
2
3
2
4
3
23
2
12
16
!1
27
64
!1
16
27
64
3
2
3
4
)3
2()
3
4()
4!
32()
"
12(
m
n
m
n
n
n
m
n
n
m
n
n
m
nmn
nm
n
=
=
=
=
=
11. (a)
62
2
6
4!
23
4
2
2
22
4
2
1
))(1
(
)()1
()()1
(
qp
q
p
qp
q
p
qpqp
qp
qp
=
=
=
(b)
6
-
8/10/2019 Chapter 01 Suggested Solution
7/19
2010 Chung Tai Educational Press. All rights reserved.
1"7
"1010
3
3
1010
3
3
22
3
6
32
33
27
2
27
64)(
32
1(
3
4)(
2
1(
)3
4()
2
1()
3
4()
2(
qp
q
p
qp
q
p
qp
q
p
qppq
qp
qp
pq
=
=
=
=
12. (a)
11
"
3
3
!
6
3
3
!
6
3
33
!
62
32
4
33
22
4
3
12
2
122
)(
)
()()
3
1()
(
q
p
q
p
q
p
p
q
q
p
p
q
q
p
p
q
q
p
pq
q
q
p
=
=
=
=
=
(b)
416
6
6
1010
6
6
1010
6
62
1010
2
3
3
22
2
23
33
2
16
32
1632
42
)4()
2()
4()
2(
qp
p
q
qp
q
p
qp
q
p
qp
q
p
qpq
qp
qp
pq
=
=
=
=
=
13. (a)
!
2
622
4
622
2
22
42
2
3
22
2
422
22
2
22
2
4
32
4
)4
2)(
2
16(
)2
)(
4(
)2
()
4(
)2
10()
4(#
)2(
10$)
4(
y
x
yxy
x
yxy
x
xyy
x
yx
xy
y
x
xy
xy
y
yx
=
=
=
=
=
(b )
16
000!
002
))((
462
))((
2
)()(
)2()(
3!
36
614
1264
246!
4
2624!4
334
2342
3
6
3
"
3
63
3
"323
qp
qp
qp
qqpp
qpqpqpqp
p
q
q
p
p
q
q
p
p
q
q
p
=
=
=
=
14. (a)
12!
2
2
2
2
2)2(
24
7
)12()62(
12
62
12
32
12
3
=
=
=
=
=
+
+
+
+
nn
n
n
n
n
n
n
(b )
4
3
33
3
2
)1()1(
1
1
=
=
= +
+
nn
n
n
7
-
8/10/2019 Chapter 01 Suggested Solution
8/19
2010 Chung Tai Educational Press. All rights reserved.
15. (a)
17
3
317
33
3123
3131!
3343
33332
343
3322
1
12
=
=
+
=
+
=
+
+
++
n
n
nn
nn
nn
nn
nn
nn
(b)
4
12
142
221
42142
213
3342
3
)13(3
)13("
333
"3"
3"
27"
a
aa
aa
aaa
aaa
aa
aa
nn
nn
nnn
nnn
nn
nn
=
=
=
+
++
++
16.
!020420
7232
112626
)(62
)(12
)(2
==
==
==
7!0100112 >>>
7!0100112 >>>
i.e. 2201006 12622 >>>
Build-up Exercise 1B(page 1.13)17. (a) 1)3( 02 =
(b)1
1)3( 220
=
=
(c)
"
2
"
16
!
1
1
!
1
)(
11
2
1)
4
3(2
16"
2
433
203
=
=
=
=
18. (a)3
22
3
33
a
aaa
=
=
(b)
2
2
)1(3
1
03
3
2
3
23
2
3
2
a
a
a
a
ba
=
=
=
(c )
2
2
22
2
22221
"
)3(
)3()3(
b
a
b
a
baba
=
=
=
19. (a)
4
4
1
44
144
14)1(3
1
1
43
2
2
)2
(
#2
$)2
(
a
b
ba
ba
ba
a
ba
=
=
=
=
(b)
11
2
112
642642))((
b
a
ba
bababa
=
=
=
+
(c )
26
26
232306
1
)(#)$(
ba
ba
bababa
=
=
=
20. (a)
36
64
!
6
4!
361
641
6
14
12
2
32
2
3
=
=
=
8
-
8/10/2019 Chapter 01 Suggested Solution
9/19
2010 Chung Tai Educational Press. All rights reserved.
(b)
2
72"
2
3
322
3
)32(2
3
)32(
1
2
3)32(
3
2
6
42
3
2
22
3
2
223
222
2
3
=
=
=
=
=
(c)
64
"
2
3
)2
3
1(
)3
2
1
1()
3
2
10
1(
6
2
2
3
1
2
1
32
1
3
0
10
=
=
=
=
21. (a)
3
2
32
2
36
42
32
202
"
3
3
)(
)3(
b
a
b
a
ba
a
ba
ba
=
=
=
(b)
7
4
74
32
422
132
22
16
16
4
)(
)4(
b
a
ba
ba
ba
ba
ab
=
=
=
(c)
!2
!222
442
42
2
1
222
22
21
16
22
2)2(
)( 2
ba
ba
ba
ba
ba
ab
=
=
=
22. (a)
3
4
432
21
1
12221221
2
27
2
33
)3
2)(3()
3
2()3(
x
y
yx
yxyxxyyx
=
=
=
(b )
12
"
12"
33
3
6"
3
36
3
323320
27
32
2
)2
3)(
2
1()
2
3()
2
1(
y
x
yx
yxyyxyx
=
=
=
(c )
3
302
22
4212
2112
1
4
2
)2
)(4()2()4(
y
yx
x
yyx
x
yyx
=
=
=
23. (a)
6
4
4
4
2
4
4
2
44222
22211202
16
16
1616
)4()4(
)4()4(
n
m
n
m
n
m
n
n
nmn
nmnm
=
=
=
=
(b )
2
14
4
!62
!
4
2
622
4
22
3
4
4
2)()
2(
m
n
m
nnm
n
mnm
n
mmn
=
=
=
9
-
8/10/2019 Chapter 01 Suggested Solution
10/19
2010 Chung Tai Educational Press. All rights reserved.
(c)
!
6
2
22
2
62
21
22
1
31
2
02
32
162
4
2)
4(#
2
)3($
m
mn
nm
n
m
n
m
n
m
n
mnm
=
=
=
24. (a)
!
6
!
62
2
4
32
26
2
16
4
)4(#
)(
4$
p
q
p
q
p
q
qpp
q
=
=
=
(b)
4
12
4124
43
143
1
023
43
16
2
)2(
#1
)2($#
)(
)2($
q
p
qp
qp
qp
qp
qp
=
=
=
=
(c)
33
21
333
213
3
21333
3711
3
3
711
61233324
!
27
2
3
3
2
)3
2(
)3
1!(
)#1!
)(3$()#1!()3$(
p
q
p
q
qp
qp
qp
pqqp
pqqp
=
=
=
=
=
=
25. (a)
4
4
11
421
32
421
1321
1
)()(
abc
c
ba
cba
ba
cba
ba
=
=
=
(b)
24
3
2
342
4222
121
422
121
221
1203
"
4
6
6
4
)(6
41
#)(6$
)4()(
ca
b
c
ba
bca
ba
bac
ba
bac
baca
=
=
=
=
(c )
3
32
1
313
442
313
412
313
2211
"
3
3
)(3#)(3$
ac
b
c
ba
cba
ba
cba
ba
cba
ba
=
=
=
=
26. (a)
3
3
3
)(3
)()3()(
13
6
622
4
6
6224
66221
42
2
233122
22
2
v
u
vvuvu
v
uvuvu
vuvuvu
vu
vuvuuv
vu
=
=
=
=
10
-
8/10/2019 Chapter 01 Suggested Solution
11/19
2010 Chung Tai Educational Press. All rights reserved.
(b)
2
2
2
)()(
)2(
32
3
3
3
42
4331
31
22
4133
u
vuv
u
vvu
vvu
vuv
vvu
=
=
=
(c)
2
2
11
2
)(2
)(2
)(
)()(#)()(2$
124
23
23
123
31
22
2
42231
13
2
2
2211123032
vu
uvvvu
uvv
vu
vuvvu
vu
vu
vu
vu
vu
uv
uv
vu
vuvuvu
=
=
=
=
=
27. (a)
!
)23()62(
23
62
23
32
23
3
)(
2
+
+
+
+
+
=
=
=
=
n
nn
n
n
n
n
n
n
(b)
7
)210(3
210
3
2
3
3
2
2
2
2
)2(
2
4
2
+
=
=
=
=
n
nn
n
n
n
n
n
n
(c)
6
)2()1(4
2
144
2
14
3
3
3
33)1(
3
3)3(
+
+
=
=
=
n
nnn
n
nnn
n
nn
28. yxyx qp 62 + and 322
2
1 + xyxqp are lie
ter&s.
)1(.................22 yxyx +=
and )2(................326 =+
xyx%ro& (1)' )3(..............03 =+ yx
%ro& (2)')4(..........12
363
=+
=+
yx
yx
(3 ) (4)'
1
)1(0)2()3(
=
=++
y
yxyx
/ustitute 1=y into (3)'
3
0)1(3
=
=+
x
x
29.
7!3"23"
!127327
!020420
3)3("
3)3(27
3)3(!1
==
==
==
7!7"!0!1
-
8/10/2019 Chapter 01 Suggested Solution
12/19
2010 Chung Tai Educational Press. All rights reserved.
(c)
3
33
3
13
27
13
27
!3!
27!3)13(
27
!333
27
!33
3
3
2
2
2
=
=
=
=
=
=
=
=
+
z
z
z
z
z
z
zz
zz
Build-up Exercise 1C(page 1.15)31. (a)
10!".
000100!".000!"
=
=
(b)310136!.2
001.0136!.2136!002.0
=
=
(c)
2
42
44
10640.!
1010640.!
10100640.!1006.!4
=
=
=
(d)
"4
""
1003.3
101003.3
101000.003.310303000.0
=
=
=
32. (a)
12
"3
"3
102.7
)1010()01.3.2(
)1001.3()10.2(
=
=
(b)
33
2310
2310
1076"."
)1010()7.701.1(
)107.()10701.1(
=
=
(c)
11
4
7
4
7
1062.2
10
10
.1
"3.3
10.1
10"3.3
=
=
(d)
3
11
!
11
!
103
10
10
303.3
"0"."
10303.3
10"0"."
=
=
33. (a)00020024
0000001042.21042.2
7
=
=
(b)22011000.0
01000.0122.110122.1
=
=
(c )00000004
0000000001.410.4
"
=
=
(d)"!"0000.0
1000.0"0".!10"0".!
4
=
=
34. (a)
12
11
!3
!3
10062.1
1062.10
)1010()".!.1(
)10".()10!.1(
=
=
=
(b)
3
36
2610
2610
10"04!.1
104!".10
)1010()""."0.1(
)10""."()100.1(
=
=
=
(c )
12
11
20
"
20
"
103
103.0
10
10
4
2.1
104
102.1
=
=
=
(d)
6
12
6
12
6
106.2
1026.0
10
10
.
43.1
10.
1043.1
=
=
=
35. (a)
027000.0
1027
)1010()3"()103()10"(
6
137137
=
=
=
12
-
8/10/2019 Chapter 01 Suggested Solution
13/19
2010 Chung Tai Educational Press. All rights reserved.
(b)
6072000.0
1026.7
)1010()3.32.2(
)103.3()102.2(
23
23
=
=
=
(c)
0000006
106.0
10
10
!
!.4
10!
10!.4
7
3
4
3
4
=
=
=
(d)
03000.0
10.3
10
10
3.2
0.!
103.2
100.!
7
12
7
12
=
=
=
36. 10 106".13 = (corr. to 3 sig. ig.)
6" 10!1.34 = (corr. to 3 sig. ig.)
67 107.36 = (corr. to 3 sig. ig.)
66 100.!7 = (corr. to 3 sig. ig.)
106"7 3746
-
8/10/2019 Chapter 01 Suggested Solution
14/19
2010 Chung Tai Educational Press. All rights reserved.
(b) Total volu&e o drin roduced in 10 da*s
101
101.2
)1010(101.2
10101.210
&101.210
6
6
3!
3!
!
>
=
=
=
=
T h e a c t o r * c a n r o d u c e d r i n o o n e
& i l l i o n l i t r e s i n 1 0 d a * s .
Build-up Exercise 1D(page 1.17)
43. (a) Place value o " 1100 ==0123 10"10110110211"2 +++=
(b) Place value o " 100102 ==0123 10410210"103"243 +++=
(c) Place value o " 10101 ==
0123410710"10100101
"710
++++=
(d) Place value o " 00010010 ==
012
46
10010106
1710!10"10260"!72
+++
+++=
44. (a)06
1061001016100012
=
++=+
(b)
201!0
10110010210010!
11100200010!
01234
=
++++=
++
(c) "!7110710!10"101 0123 =+++
(d)
0"030
10010"
10010010310
10"10310
01
234
14
=
++
+++=
++
45. (a) Place value o 0
2
21
=
=
(b) Place value o 0
1
20
=
=
(c ) Place value o 0
!
23
=
=
(d) Place value o 0
16
24
=
=
46. (a) Place value o 1
2
21
=
=
(b) Place value o 1
4
22
=
=
(c ) Place value o 1
!
23
=
=
(d) Place value o 1
32
2
=
=
47. (a) Place value o the let&ost digit
100102 ==
Place value o the right&ost digit
1100 ==
u&er o ti&es
100
1
100
=
=
(b) Place value o the let&ost digit
000110 3 ==
Place value o the right&ost digit
10101 ==
u&er o ti&es
100
10
0001
=
=
(c ) Place value o the let&ost digit
000000110 6==
Place value o the right&ost digit
100102 ==
u&er o ti&es
00010
100
0000001
=
=
(d) Place value o the let&ost digit
14
-
8/10/2019 Chapter 01 Suggested Solution
15/19
2010 Chung Tai Educational Press. All rights reserved.
100102 ==
Place value o the right&ost digit
10101 ==
u &er o ti&es1010
100
=
=
48. (a) Place value o the let&ost digit 0 !
23
=
=
Place value o the right&ost digit 0 1
20
=
=
u &er o ti&es
!
1
!
=
=
(b) Place value o the let&ost digit 0 4
22
=
=
Place value o the right&ost digit 0 2
21
=
=
u &er o ti&es
2
2
4
=
=
(c) Place value o the let&ost digit 0
32
2
=
=
Place value o the right&ost digit 0 1
20
=
=
u &er o ti&es
32
1
32
=
=
(d) Place value o the let&ost digit 0 16
24
=
=
Place value o the right&ost digit 0
2
21
=
=
u &er o ti&es
!
2
16
=
=
49. (a) Place value o the let&ost digit 1 !
23
=
=
Place value o the right&ost digit 1 2
21
=
=
u&er o ti&es
4
2
!
=
=
(b ) Place value o the let&ost digit 1 1624
=
=
Place value o the right&ost digit 1 1
20
=
=
u&er o ti&es
16
1
16
=
=
(c ) Place value o the let&ost digit 1 32
2
=
=
Place value o the right&ost digit 1 4
22
=
=
u&er o ti&es
!
4
32
=
=
(d ) Place value o the let&ost digit 1 32
2
=
=
Place value o the right&ost digit 1 2
21
=
=
u&er o ti&es
16
2
32
=
=
50. (a) 0122 212121111 ++=
(b ) 01232 212120211011 +++=
(c )01234
2
212020212111001 ++++=
(d )01
2342
2021
21212021101110
++
+++=
51. (a)
2
0123
1101
21202121
1141!1
=
+++=
++
15
-
8/10/2019 Chapter 01 Suggested Solution
16/19
2010 Chung Tai Educational Press. All rights reserved.
(b)
2
01234
11000
2020202121
20!1161
=
++++=
++
(c)
2
01
234
24
110100
2020
21202121
212121
=
++
+++=
++
(d)
2
01
234
124
110010
2021
20202121
21202121
=
++
+++=
+++
52. (a)
6
24
22
202121110
12
0122
=
+=
+=
++=
(b)
14
24!
222
202121211110
23
01232
=
++=
++=
+++=
(c)
36
432
22
2020
21202021100100
2
01
2342
=
+=
+=
++
+++=
(d)
!0
1664
22
2020
2020212021
1010000
46
01
2346
2
=
+=
+=
++
++++=
53. (a) ivide 4 * 2 continuousl*' +e get
1
, e & a i n d e r
0
1
1
0
222
42
112
2
22
1
21011014 =
(b) ivide 6" * 2 co ntinuousl*' +e get
1
, e & a i n d e r
0
1
0
0
342
6"2
172
!2
42
2
0
2
1
210001016" =
(c ) ivide !3 * 2 co ntinuousl*' +e get
1
, e & a i n d e r
1
0
01
412
!32
202
102
22
0
2
1
21010011!3 =
(d) ivide 130 * 2 continuousl*' +e get
0
, e & a i n d e r
1
0
0
0
62
1302
322
162
!2
4
0
0
22
1
2
210000010130 =
54. (a) argest denar* nu&er 420"6 =
/&allest denar* nu&er 6"204 =
(b) Place value o digit 2 o "6 420 10101 ==
Place value o digit 2 o 204
6"
16
-
8/10/2019 Chapter 01 Suggested Solution
17/19
2010 Chung Tai Educational Press. All rights reserved.
00010010 ==
55. argest 6digit inar* nu&er 2111000=
/&allest 6digit inar* nu&er 2100011=
56. (a) /uggested ans+er
4' ! and 12 are three &ultiles o 4.
ivide 4 * 2 con tinuousl*' +e get
0
, e & a i n d e r
0
22
42
1
21004 =
ivide ! * 2 con tinuousl*' +e get
0, e & a i n d e r
0
42!2
22
1 0
21000! =
ivide 12 * 2 co ntinuousl*' +e get
0
, e & a i n d e r
0
1
62
122
32
1 2110012 =
( b ) T h e l a s t t + o d i g i t s o t h e i n a r * n u
& e r s
o t a i n e d i n ( a ) a r e 0 .
Build-up Exercise 1E(page 1.19)
57. (a) Place value o A
16
161
=
=
(b) Place value o A
1
160
=
=
(c) Place value o A
26
162
=
=
(d) Place value o A
0"64
16
3
=
=
58. (a) 0116 1611167-7 +=
(b ) 01216 1601661660 ++=
(c ) 01216 161216141613EC ++=
(d )0123
16 161416131601612C0E +++=
59. (a) Plac e v alu e o the le t&o st nu& era l
- 16
161
=
=
Place value o the r ight&ost nu&era l
- 1
160
=
=
u&er o ti&es
16
1
16
=
=
(b ) Place value o the let&ost nu&eral
- 0"64
16
3
=
=
Place value o the r ight&ost nu&eral
- 1
160
=
=
u&er o ti&es
0"64
1
0"64
=
=
(c ) Place value o the let&ost nu&eral
- 0"64
16
3
=
=
Place value o the r ight&ost nu&eral
- 16
161
=
=
u&er o ti&es
26
16
0"64
=
=
(d ) Place value o the let&ost nu&eral
- 366
16
4
=
=
17
-
8/10/2019 Chapter 01 Suggested Solution
18/19
2010 Chung Tai Educational Press. All rights reserved.
Place value o the r ight&ost nu&era l
- 16
161
=
=
u&er o ti&es0"64
16
366
=
=
60. (a) ivide 16 * 16 continuousl*' +e get
0
, e & a i n d e r
1
1616
161016 =
ivide
2
16
* 16 continuo us l*' +e get
0
, e & a i n d e r
0
1616
16216
1
162
10016 =
ivide 316 * 16 cont inuous l*' +e ge t
0
, e & a i n d e r
0
16216
16316
16
0
16
1
163
100016 =
ivide 416 * 16 cont inuous l*' +e ge t
0
, e & a i n d e r
0
16316
16416
162
0
16
16
0
16
1
164 1000016 =
(b) 166
100000016 =
61. (a)
60
12163
1612163C3 0116
=
+=
+=
(b)
4"6
161261
1601611610%1 01216
=
+=
++=
(c )
!3!
6164263
166164163346 01216
=
++=
++=
(d)
"661
1416126100"6412
161416116101612
CA%E
0123
16
=
+++=
+++=
62. (a) ivide 3 * 16 continuousl*' +e get
3
, e & a i n d e r
2
316
16233 =
(b) ivide 12 * 16 continuousl*' +e get
0
, e & a i n d e r
0
3216
1216
2
1620012 =
(c ) ivide 2334 * 16 continuousl*' +e get
14(E)
, e & a i n d e r
11416
2 33416
"
16E"13342 =
(d) ivide 11003 * 16 con tinuousl*' +e get
11(-)
, e & a i n d e r
1(%)
10(A)
6!716
11 00316
4216
2
16A%-200311
=
63. (a) %irstl*' convert 211000 into a denar*
nu&er.
24
!16
22
2020202121
11000
34
01234
2
=
+=
+=
++++=
Then' convert 24 into a he8adeci&al nu&er.
18
-
8/10/2019 Chapter 01 Suggested Solution
19/19
ivide 24 * 16 continuousl*' +e get
!
, e & a i n d e r
1
2416
16
1!24 =
i.e. 162 1!11000 =
(b) %irstl*' convert 210001110 into a denar*
nu&er.
142
24!12!
2222
202121
2120202021
10001110
1237
012
3467
2
=
+++=
+++=
+++
++++=
Then' convert 142 into a he8ade ci&al nu&er.
ivide 142 * 16 continuousl*' +e get
14(E)
, e & a i n d e r
!
14216
16E!142 =
i.e. 162 E!10001110 =
64. (a) %irstl*' convert 16113 into a denar* nu&er.
27
3161261
163161161113012
16
=
++=
++=
Then' convert 27 into a inar* nu&er.
ivide 27 * 2 continuousl*' +e get
1
, e & a i n d e r
1
0
0
1
1372
272
6!2
342
172
!
0
0
42
2
2
0
2
1
210001001127 =
i.e. 216 100010011113 =
(b ) %irstl*' convert 16C2 into a denar* nu&er.
44
12162
1612162C201
16
=
+=
+=
Then' convert 44 into a inar* nu&er.
ivide 44 * 2 continuousl*' +e get
0
, e & a i n d e r
0
1
1
0
222
442
112
2
22
1
210110044 =
i.e. 216 101100C2 =
65. (a) argest he8adeci&al nu&er 16"70%A=
/&allest he8adeci&al nu&er 16A%07"=
(b ) Place value o nu&eral A o 16"70%A
366
16
4
=
=
Place value o nu&eral A o 16A%07"
16
161
=
=
