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vd89/gist:83b19e60c61c408c97a84455eeb19578

Last active March 20, 2020 07:12
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The Number System from BootCamp
Raw
gistfile1.txt
Question and answer for the problem set
1. What is the Decimal equivalent of (​11110000101010101​)2
Ans. 1 * 2^16 = 65536
1 * 2^15 = 32768
1 * 2^14 = 16384
1 * 2^13 = 8192
0 * 2^12 = 0
0 * 2^11 = 0
0 * 2^10 = 0
0 * 2^9 = 0
1 * 2^8 = 256
0 * 2^7 = 0
1 * 2^6 = 64
0 * 2^5 = 0
1 * 2^4 = 16
0 * 2^3 = 0
1 * 2^2 = 4
0 * 2^1 = 0
1 * 2^0 = 1
sum = (1+4+16+64+256+8192+16384+32768+65536)
Decimal = (123221)10
2.What is the Hexadecimal equivalent of (98899910)10
Ans.
98989910
6186869 6
386679 5
24167 7
1510 7
94 6
5 14
Hexadecimal => (5E67756)16
Hexadecimal
0-9
10 - A
11 - B
12 - C
13 - D
14 - E
15 - F
Raw
gistfile2.txt
6.Convert the following​ floating numbers
1) (34.34)​ 10
2) (125.125)​ 10
3) (10.16)​ 10
to ​ binary, base 3, octal, and hexadecimal.​ Any fractions
that do not terminate should be truncated to 4 digits in
the fractional part.
1) (34.34)​10
2/ 34 Exponent
17 0
8 1
4 0
2 0
1 0
0.34 Mantissa
0.34 * 2 = 0.68
0.68 * 2 = 1.36
0.38 * 2 = 0.72
0.72 * 2 = 1.44
0.44 * 2 = 0.88
0.88 ----
(34.34)10 = (100010.01010)2
3/ 34
11 1
3 2
1 0
0.34 * 3 = 1.02
0.02 * 3 = 0.06
0.06 * 3 = 0.18
0.18 * 3 = 0.54
0.54 * 3 = 1.62
0.62 * 3 = 1.85
0.85 * 3 = 2.55
0.55 * 3 = 1.65
0.65 * 3 = ----
(34.34)10 = ( 1021.10001121)3
8/ 34
4 2
0.34 * 8 = 2.72
0.72 * 8 = 5.76
0.76 * 8 = 6.08
0.08 * 8 = 0.64
0.64 * 8 = 5.12
0.12 * 8 = 0.96
0.96 * 8 = 7.68
0.68 * 8 = 5.44
(34.34)10 = (42.25605075)
16/ 34
2 2
0.34 * 16 = 5.44
0.44 * 16 = 7.04
0.04 * 16 = 0.64
0.64 * 16 = 10.24
0.24 * 16 = 3.84
0.84 * 16 = 13.44
0.44 * 16 = 7.04
(34.34)10 = (22.570A3D7)
2) (125.125)10
2/ 125
62 1
31 0
15 1
7 1
3 1
1 1
0.125 * 2 = 0.25
0.25 * 2 = 0.50
0.50 * 2 = 1.0
0 ---
(125.125)10 = (1111 101.001)2
3/ 125
41 2
13 2
4 1
1 1
0.125 * 3 = 0.375
0.375 * 3 = 1.125
0.125 * 3 = 0.375
0.375 * 3 = 1.125
----
(125.125)10 = (11122.0101)3
8/ 125
15 5
1 7
0.125 * 8 = 1.000
000---
(125.125)10 = (175.10)8
16/ 125
7 13 D
0.125 * 16 = 2.0
0.000
(125.125)10 = (7D.20)16
3) (10.16)​ 10
2/ 10
5 0
2 1
1 0
0.16 * 2 = 0.32
0.32 * 2 = 0.64
0.64 * 2 = 1.28
0.28 * 2 = 0.56
0.56 * 2 = 1.12
0.12 * 2 = 0.24
0.24 * 2 = 0.48
0.48 * 2 = 0.96
0.96 * 2 = 1.92
----
(10.16)10 = (1010.001010001)2
3/ 10
3 1
1 0
0.16 * 3 = 0.48
0.48 * 3 = 1.44
0.44 * 3 = 1.32
0.32 * 3 = 0.96
0.96 * 3 = 2.88
0.88 * 3 = 2.64
0.64 * 3 = 1.92
(10.16)10 = (101.0110221)3
8/ 10
1 2
0.16 * 8 = 1.28
0.28 * 8 = 2.24
0.24 * 8 = 1.92
0.92 * 8 = 7.36
0.36 * 8 = 3.24
0.24 * 8 = 1.92
(10.16)10 = (12.121731)8
16/ 10
0.16 * 16 = 2.56
0.56 * 16 = 8.96
0.96 * 16 = 15.36
0.36 * 16 = 5.76
0.76 * 16 = 12.16
0.16 * 16 = 2.56
(10.16)10 = (A.28F5C2)16
Raw
gistfile3.txt
5.Convert the following base 10 numbers to the base indicated:
A. (5610)​ 10 ​ => ( )​ 2
B. (5610)​10 => ( )​ 3
C. (5610)​ 10 => ( )​ 8
D. (5610)​ 10​ => ( )​ 12
E. (5610)​ 10 => ( )​ 16
F. (22110)​ 10​ => ( )​ 2
G. (22110)​ 10​ ​ => ( )​ 3
H. (22110)​ 10 => ( )​ 8
I. (22110)​ 10​ => ( )​ 12
J. (22110)​ 10​ => ( )​ 16
A. (5610)​ 10 ​ => ( )​ 2
2/ 5610
2805 0
1402 1
701 0
350 1
175 0
87 1
43 1
21 1
10 1
5 0
2 1
1 0
(5610)10 = (1010 1111 0101 0)2
B. (5610)​10 => ( )​ 3
3/ 5610
1870 0
623 1
207 2
69 0
23 0
7 2
2 1
(5610)10 = (21200210)3
C. (5610)​10 => ( )​8
8/ 5610
701 2
87 5
10 7
1 2
(5610)10 = (12752)8
D. (5610)​ 10​ => ( )​ 12
12/ 5610
467 6
38 11
3 2
(5610)10 = )32B6
E. (5610)​ 10 => ( )​16
16/ 5610
350 10 A
21 14 E
1 5
(5610)10 = (15EA)16
F. (22110)​ 10​ => ( )​2
2/ 22110
11055 0
5527 1
2763 1
1381 1
690 1
345 0
172 1
86 0
43 0
21 1
10 1
5 0
2 1
1 0
(22110)10 = (1010 1100 1011 110)2
G. (22110)​ 10​ ​ => ( )​ 3
3/ 22110
7370 0
2456 2
818 2
272 2
90 2
30 0
10 0
3 1
1 0
(22110)10 = (1010 0222 20)3
H. (22110)​ 10 => ( )​ 8
8/ 22110
2763 6
345 3
43 1
5 3
(22110)10 = (53136)
I. (22110)​ 10​ => ( )​ 12
12/ 22110
1842 6
153 6
12 9
1 0
(22110)10 = (10966)12
J. (22110)​ 10​ => ( )​ 16
16/ 22110
1381 14 E
86 5
5 6
(22110)10 = (565E)
Raw
gistfile4.txt
4.Convert the following numbers to the ​ base 10​ :
A. (3312)8
B. (167)8
C. (202103)9
D. (3132334)16
E. (0xF2)16
A. (3312)8
3 * 8^3 = 1536
3 * 8^2 = 192
1 * 8^1 = 8
2 * 8^0 = 2
1536+192+8+2 = (1738)10
(3312)8 == (1738)10
B. (167)8
1 * 8^2 = 64
6 * 8^1 = 48
7 * 8^0 = 7
64+48+7 =(119)10
(167)8 = (119)10
C. (202103)9
2 * 9^5 = 118098
0 * 9^4 = 0
2 * 9^3 = 1458
1 * 9^2 = 81
0 * 9^1 = 0
3 * 9^0 = 3
118098+1458+81+3 =(119640)10
(202103)9 = (119640)10
D. (3132334)16
3 * 16^6 = 50331648
1 * 16^5 = 1048576
3 * 16^4 = 196608
2 * 16^3 = 8192
3 * 16^2 = 768
3 * 16^1 = 48
4 * 16^0 = 4
50331648+1048576+196608+8192+768+48+4 = (51585844)10
(3132334)16 = (51585844)10
E. (0xF2)16
F * 16^1 = 240
2 * 16^0 = 2
240+2 = (242)10
(0xF2)16 =(242)10
Raw
gistfile5.txt
3.Convert the following numbers to base indicated and
vice-versa (Cross-Verify)
A. (1101)2​ => ( )8
B. (1111 1111 1110)2​ => ( )10
C. (221201)3​ => ( )10
D. (76)8​ => ( )10
E. (231)8​ => ( )2
F. (0xF00)16​ => ( )8
G. (0xDACE)16 ​ => ( )12
H. (0x2B)16 =>( )8
A. (1101)2​ => ( )8
1 * 2^3 = 8
1 * 2^2 = 4
0 * 2^1 = 0
1 * 2^0 = 1
(1101)2 = (13)10
13
13/8 1 5
(1101)2 == (13)10 == (15)8
B. (1111 1111 1110)2​ => ( )10
1 * 2^11 = 2048
1 * 2^10 = 1024
1 * 2^9 = 512
1 * 2^8 = 256
1 * 2^7 = 128
1 * 2^6 = 64
1 * 2^5 = 32
1 * 2^4 = 16
1 * 2^3 = 8
1 * 2^2 = 4
1 * 2^1 = 2
0 * 2^0 = 0
2+4+8+16+32+64+128+256+512+1024+2048 = (4094)10
(1111 1111 1110)2​ => (4094)10
C. (221201)3​ => ( )10
2 * 3^5 = 486
2 * 3^4 = 162
1 * 3^3 = 27
2 * 3^2 = 9
0 * 3^1 = 0
1 * 3^0 = 1
1+9+27+162+486 = (685)10
(221201)3​ => (685)10
D. (76)8​ => ( )10
7 * 8^1 = 56
6 * 8^0 = 6
56+6 = (62)10
(76)8​ => (62)10
E. (231)8​ => ( )2
2 * 8^2 = 128
3 * 8^1 = 24
1 * 8^0 = 1
1+24+128 = (153)10
153
76 1
38 0
19 0
9 1
4 1
2 0
1 0
(153)10 => (10011001)2
(231)8​ => (10011001)2
F. (0xF00)16​ => ( )8
F * 16^2 = 15 * 16^2 = 3840
0 * 16^1 = 0
0 * 16^0 = 0
(0xF00)16 = (3840)10
8/ 3840
480 0
60 0
7 4
(3840)10 = (7400)8
G. (0xDACE)16 ​ => ( )12
D * 16^3 = 13 * 16^3 = 53248
A * 16^2 = 10 * 16^2 = 2560
C * 16^1 = 12 * 16^1 = 192
E * 16^0 = 14
(0xDACE)16 = (56014)10
12/ 56014
4667 10
388 11
32 4
2 8
(AB482)12
(0xDACE)16 ​ => (AB482)12
H. (0x2B)16 =>( )8
2 * 16^1 = 32
B * 16^0 = 11
(2B)16 = (43)10
8/ 43
5 3
(0x2B)16 = (53)8
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