1. The document discusses converting between binary, decimal, and hexadecimal number systems by explaining place value and how to perform conversions using addition and multiplication by powers of two. 2. It provides examples of converting specific values such as 221 between decimal and binary as well as between decimal, binary, and hexadecimal. 3. The examples demonstrate how to identify the place value of each digit and then add or multiply the place value amounts to obtain the value in the target number system.

1. F ก
ก :
กก : ก F Weight ก F 1 กก F
F : (11011101)2 F
(11011101)2 = (1X27) + (1X26) + (0X25) + (1X24) + (1X23)+ (1X22) +
(0X21) + (1X20)
= 128 + 64 + 0 + 16 + 8 + 4 + 0 + 1
= (221)10
F : (1011.101)2
1 0 1 1 . 1 0 1 F
2-3 0.125
2-2 0.0
2-1 0.5
-
20 1.
21 2.
22 0.
23 8.
(11.625)10
∴ (1011.101)2 = (11.625)10
ก
กก
1. F 2 F F F F
(LSB)
2. F F กF 1 F 2 ก
3. F 2 F F F F
ก (MSB)

2. F : (221)10
2 221 1 (LSB)
2 110 0
2 55 1
2 27 1
2 13 1
2 6 0
2 3 1
2 1 1 (MSB)
0
∴ (221)10 = (11011101)2
F ก (Weight) F
F (221)10 = ( )2
1. F ก (Weight) Weight F ก F Fก
128 128 64 32 16 8 4 2 1
2. ก F Weight F ก F Weight ก F F F
Fก F ก
F Weight 128 64 32 16 8 4 2 1
ก 128 + 64 + 0 + 16 + 8 + 4 + 0 + 1 = 221
1 1 0 1 1 1 0 1
∴ (221)10 = (11011101)2
ก
กก
1. 1. F F F ก F F
2. 2. F F F 2 F F กF 1 F F
0 FF F กก F 1 Fก 1 F F 1
3. 3. F F ก ก F 2
F F ก F ก ก F กF F
Fก 1 F F F F
F : (0.375)10

3. ก
0.375 X 2 = 0.75 0
0.75 X 2 = 1.5 1
0.5 X 2 = 1.0 1
(0.375)10 = (0.011)2
F : (12.35)10
1. 1. (12)10 F
(12)10 = (1100)2
2. (0.35)10
ก
0.35 X 2 = 0.7 0
0.7 X 2 = 1.4 1
0.4 X 2 = 0.8 0
0.8 X 2 = 1.6 1
0.6 X 2 = 1.2 1
0.2 X 2 = 0.4 0
0.4 X 2 = 0.8 0
0.8 X 2 = 1.6 1
ก ก F 6
(12.35)10 = (1100.010110)2
ก
ก
กก F: F ก (Weight) F
ก F F ก ก ก
ก : Weight F กF 84 83 82 81 80 8-1 8-2 8-3
F : (134)8 = ( )10
(134)8 = (1X82) + (3X81) + (4X80)
= 64 + 24 + 4
= (92) 10
(134)8 = (92)10

4. ก
กก F: F F 8 F กก
F F ก ก
F : (92)10 = ( )8
8 92 4
8 11 3
8 1 1
0
1 3 4
(92)10 = (134)8
ก
ก
กก : F F ก ก
F : (134)8 = ( )2
1.
(134)8 = (1X88) + (3X81) + (4X80)
= (92)10
2.
(92)10 = ( )2
Weight = 64 32 16 8 4 2 1
= 64 + 0 + 16 + 8 + 4 + 0 + 0
2 =1 0 1 1 1 0 0
(134)8 = (1011100)2
ก
กก : F F ก ก
F : (1011100)2 = ( )8
1. 1.
(1011100)2 = 64 + 0 + 16 + 8 + 4 + 0 + 0
= (92)10
2. 2.

5. 8 92 4
8 11 3
8 1 1
0
1 3 4
(1011100)2 = (134)8
ก
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111
ก F ก F 3
F :
(1011100) 2 = ( )8
: 001 011 100
1 3 4
(1011100) 2 = (134)8
F
(6143)8 = ( )2
6 1 4 3
110 001 100 011
(6143)8 = (110001100011)2

6. ก ก ก
ก ก
กก : F ก (Weight) ก F
ก F ก ก ก
ก (Weight) : 164 163 162 161 160 16-1 16-2 16-3
F (6C)16 = ( )10
(6C)16 = (5X161) + (12X160)
= 80 + 12
= (92)10
(6C)16 = (92)10
F (0.3)16 = ( )10
(0.3)16 (0.3)16 = 3X10-1
= 3X0.0625
= (0.1875)10
(0.3)16 = (0.1878)10
ก ก
กก : F 16 F กก F
ก F ก ก
F : (92)10 = ( )16
: 16 92 12 =C
16 5 5
5 C
(92)10 = (5C)16
F (0.7875)10 = ( .)16
ก
0.7875 X 16 = 12.6 12 = C
0.6 X 16 = 9.6 9
0.6 X 16 = 9.6 9
0.6 X 16 = 9.6 9
(0.7875)10 = (0.C9)16

7. ก ก ก
ก
กก : F F ก
F : (5C)16 = ( )2
1. ก
(5C)16 = (5X161) + (12X160)
= 80 + 12
= (92)10
2.
(92)10 = ( )2
Weight = 64 32 16 8 4 2 1
64 + 0 + 16 + 8 + 4 + 0 + 0
=1 0 1 1 1 0 0
(5C)16 = (1011100)2
ก ก
กก : F F ก
F : (1011100)2 = ( )16
1. (1011100)2
(1011100)2 = (92)10
2. ก
16 92 12 =C
16 5 5
0
5 C
(1011100)2 = (5C)16

8. ก ก ก
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
A 1010
B 1011
C 1100
D 1101
E 1110
F 1111
กก
ก F ก ก F 4
F (1011100)2 ก
0101 1100
5 12
5 C
(1011100)2 = (5C)16
F (1011110111011)2 ก
0001 0111 1011 1011
1 7 11 11
1 7 B B
(1011110111011)2 = (17BB)16
F (A95)16
A 9 5
1010 1001 0101
(A95)16 = (101010010101)2

9. แบบฝกหัด
2.1 F (base-4) F (base-5)
a. 10 b. 21
c. 50 d. 67
e. 100
2.2 F
a. (24)5 b. (3F7)16
c. (148)8 d. (ABC)15
2.3 F F 4 F
a. (0.1111)2 b. (0.11010011)2
c. (001110.111111111)2
2.4 F F 4 F
a. (0.1111)10 b. (947.613)10
c. (4287.6543)10
2.5 ก F
a. (ABCE)16 b. (97F)16
c. (A0)16
2.6 F ก
a. (375)8 b. (054)8
c. (3517)8