19. Show that the fractional error of a quantity given by the product of two
quantities is the sum of the fractional error of the two quantities.
Answers
How to convert decimal to binary
Conversion steps:
Divide the number by 2.
Get the integer quotient for the next iteration.
Get the remainder for the binary digit.
Repeat the steps until the quotient is equal to 0.
Example #1
Convert 1310 to binary:
Division
by 2 Quotient Remainder Bit #
13/2 6 1 0
6/2 3 0 1
3/2 1 1 2
1/2 0 1 3
So 1310 = 11012
Example #2
Convert 17410 to binary:
Division
by 2 Quotient Remainder Bit #
174/2 87 0 0
87/2 43 1 1
43/2 21 1 2
21/2 10 1 3
10/2 5 0 4
5/2 2 1 5
2/2 1 0 6
1/2 0 1 7
So 17410 = 101011102
Decimal to binary conversion table
Decimal
Number Binary
Number Hex
Number
0 0 0
1 1 1
2 10 2
3 11 3
4 100 4
5 101 5
6 110 6
7 111 7
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F
16 10000 10
17 10001 11
18 10010 12
19 10011 13
20 10100 14
21 10101 15
22 10110 16
23 10111 17
24 11000 18