BASE CONVERSION HELP PLEASE! Conversion among various bases . a) (103.8) 10 =(
ID: 668779 • Letter: B
Question
BASE CONVERSION HELP PLEASE!
Conversion among various bases.
a) (103.8)10 =( ? )3
b) (103.8)10 = ( ? )9 hint: can you calculate quickly from the result of a)?
c) (85.7)10 = ( ? )2 = ( ? )4 = ( ? )8 = ( ? )16
d) (14.1)5 = (?)10 = ( ? )6
e) (12110.1)3 = ( ? )9
Addition and Subtraction
a) (1A.34 + 4.F )16
b) (343.24 - 241.21)5
c) (87.43 - 285.78)9
d) (10110 – 1110.1)2
e) (10110 – 1110.1)3
f) (10110 – 1110.1)10
g) (10110 – 1110.1)16
Explanation / Answer
Conversion among bases:
To convert a whole number from decimal to base x:
Just repeatedly divide the number with x and store the result in a stack.
Update the quotient as the new number and repeat till the quotient becomes 0.
Finally Considering all the digits in LastInFirstOut order will generate the whole number equivalent to the base x.
To convert a fractional number from decimal to base x:
Just repeatedly multiply the fractional part with x, and add the integral part of the result to the right of the decimal.
Update the fractional part of the result as the new fractional value and repeat till the required number of decimal values or till the fraction becomes 0.
a. 103.810 = ?3.
Quotient Remainder
103
34 1
11 1
3 2
1 0
0 1
Therefore the integral part is 10211
Fractional part:
.8 * 3 = 2.4 (Result: 10211.2*****)
.4 * 3 = 1.2 (Result: 10211.21****)
.2 * 3 = 0.6 (Result: 10211.210***)
.6 * 3 = 1.8 (Result: 10211.2101**)
.8 * 3 = 2.4 (Result: 10211.21012)
Therefore 103.810 = 10211.210123.
b. 103.810 = ?9
Quotient Remainder
103
11 4
1 2
0 1
Therefore the integral part is 124
Fractional part:
.8 * 9 = 7.2 (Result: 124.7)
.2 * 9 = 1.8 (Result: 124.71)
.8 * 9 = 7.2 (Result: 124.717171)
Therefore 103.810 = 124.7171719.
c. 85.710 = ?2 = ?4 = ?8 = ?16
Quotient Remainder
85
42 1
21 0
10 1
5 0
2 1
1 0
0 1
Therefore integral part is: 1010101
Fractional part:
.7 * 2 = 1.4
.4 * 2 = 0.8
.8 * 2 = 1.6
.6 * 2 = 1.2
.2 * 2 = 0.4
Therefore 85.710 = 1010101.101102
Quotient Remainder
85
21 1
5 1
1 1
0 1
Therefore integral part is: 1111
Fractional part:
.7 * 4 = 2.8
.8 * 4 = 3.2
.2 * 4 = 0.8
.8 * 4 = 3.2
Therefore 85.710 = 1111.2303034
Quotient Remainder
85
10 5
1 2
0 1
Therefore integral part is: 125
Fractional part:
.7 * 8 = 5.6
.6 * 8 = 4.8
.8 * 8 = 6.4
.4 * 8 = 3.2
.2 * 8 = 1.6
.6 * 8 = 4.8
Therefore 85.710 = 125.5463148
Quotient Remainder
85
5 5
0 5
Therefore integral part is: 55
Fractional part:
.7 * 16 = 11.2
.2 * 16 = 3.2
.2 * 16 = 3.2
Therefore 85.710 = 55.B3333316.
d. 14.15 = ?10 = ?6
4 * 50 + 1 * 51 = 9
Therefore integral part is: 9.
Converting the fractional part.
1 * (1/(51)) = .2
Therefore 14.15 = 9.210
Quotient Remainder
9
1 3
0 1
Therefore integral part is: 13.
Converting the fractional part.
.2 * 6 = 1.2
.2 * 6 = 1.2
Therefore 14.15 = 9.210 = 13.1116
e. 12110.13 = ?9
0*30 + 1*31 + 1* 32 + 2* 33 + 1* 34 + 1 * 1/31 = 147.3
Quotient Remainder
147
16 3
1 7
0 1
Therefore the integral part is: 173.
The fractional part is:
.33 * 9 = 2.7
.7 * 9 = 6.3
Therefore 12110.13 = 173.29
Addition and Subtractions:
a. (1A.34 + 4.F )16 = 1F.2416
b. (343.24 - 241.21)5 = 102.035
c. (87.43 - 285.78)9 =
d. (10110 – 1110.1)2 = 111.12
e. (10110 – 1110.1)3 = 1222.23
f. (10110 – 1110.1)10 = 8999.910
g. (10110 – 1110.1)16 = EFFF.F16
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