 # NUMBER BASES CONT.

Welcome to class!

In today’s class, we will be talking about number bases. Enjoy the class!

### NUMBER BASES #### Binary Subtraction:

The subtraction of the binary digit depends on the four basic operations

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

The above first three operations are easy to understand as they are identical to decimal subtraction. The fourth operation can be understood with the logic two minus one is one.

For a binary number with two or more digits, the subtraction is carried out column by column as in decimal subtraction. Also, sometimes one has to borrow from the next higher column. Consider the following example.

The above subtraction is carried out through the following steps.

0 – 0 = 0

For 0 – 1 = 1, taking borrow 1 and then 10 – 1 = 1

For 1 – 0, since 1 has already been given, it becomes 0 – 0 = 0

1 – 1 = 0

Therefore, the result is 0010.

• ##### Multiplication of two digits binary numbers:

Problem solving on quantitative aptitude related to conversion and application in real life situations

Binary multiplication is actually much simpler to calculate than decimal multiplication. In the case of decimal multiplication, we need to remember 3 x 9 = 27, 7 x 8 = 56, and so on. In binary multiplication, we only need to remember the following,

0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1

Note that since binary operates in base 2, the multiplication rules we need to remember are those that involve 0 and 1 only. As an example of binary multiplication, we have 101 times 11,

101
x11

Firstly, we multiply 101 by 1, which produces 101. Then we put a 0 as a placeholder as we would in decimal multiplication, and multiply 101 by 1, which produces 101.

101
x11

101
1010 <– the 0 here is the placeholder

The next step, as with decimal multiplication, is to add. The results from our previous step indicates that we must add 101 and 1010, the sum of which is 1111.

101
x11
101
1010
1111

In our next class, we will be talking about Basic Operations.  We hope you enjoyed the class.

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