Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016 Page 6
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135.1
Converting Binary to Decimal
To convert a binary number to its decimal form, follow these 3 simple steps:
Write out the number - but leave lots of space between your digits, like this:
1
0
0
1
Multiply each number by a 2, and starting with an exponent of 0 on the very last 2, and
increase the exponent by 1 each time, like this:
3
2
1
0
[1
(2
)] [0
(2
)] [0
(2
)] [1
(2
)]
Sum them up and calculate:
3
2
1
0
[1
(2
)] + [0
(2
)] + [0
(2
)] + [1
(2
)]
=[1
(8)] + [0
(4)] + [0
(2)] + [1
(1)]
=8 + 0 + 0 + 1 = 9
Exercise 5: Convert each of the follwing binary numbers to decimal form.
2
1
0
(a) 110
1(2
) + 1(2
) + 0(2
) = 4 + 2 + 0 = 6
2
1
0
(b) 101
1(2
) + 0(2
) + 1(2
) = 4 + 0 + 1 = 5
4
3
2
1
0
(c) 00111
0(2
) + 0(2
) + 1(2
) + 1(2
) + 1(2
) = 4 + 2 + 1 = 7
5
0
(d) 100001
1(2
) + 0 + 0 + 0 + 0 + 1(2
) = 32 + 1 = 33
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