Lesson 1, Topic 5
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Subtraction in Other Bases

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Topic Content:

• Subtraction in Other Bases

Reminder of the rules of binary subtraction:

0 – 0 = 0
1 – 0 = 1
1 – 1 = 0
10 – 1 = 1
11 – 1 = 10

When you borrow a number during subtraction, it becomes the number of the base you are subtracting from.

For example, in Base 2 if you borrow a number the number you borrow becomes 2, Likewise in base 5 if you borrow a number it becomes 5.

Now, let’s take some examples.

Examples 1.5.1:

Evaluate the following:

1. 11000two – 111two
2. 20204six – 5125six
3. 72438 – 45368
4. 1A3516 – F7E16

1. 11000two – 111two

Solution

Explanation

1st Column (from right to left): 0 is smaller than 1 so we will have to borrow from the 2nd column. Since it is in base 2 any number borrowed is 2. So borrowing two from the second will give (2 + 0) – 1 = 1

2nd Column: This reduces 0 to -1 in the second column. -1 is smaller than 1 so we have to borrow again from the third column. We now have:

= 2 + (- 1) – 1
= 1 -1
= 0

3rd Column: This also reduces 0 to – 1 in the 3rd column. This too is smaller than 1 so like the second column what we have is 2 – 1 – 1 = 0

4th Column: This reduces 1 to 0 in the fourth column. We then have 0 – 0 = 0

5th Column: This column requires no borrowing since 1 is greater than 0. We simply have 1 – 0 = 1

This yields 10001two

2. 20204six – 5125six

Solution

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Responses

1. Becoming simpler by the lesson