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#Problem Solving & Logical Reasoning
Let’s CatCh Up
Convert (26) to a binary number and write answer below.
10
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i + BINARY TO DECIMAL CONVERSION
To convert a binary number into a decimal number, follow the given steps:
Step 1: Multiply each digit of the binary number by 2 to the power of n, where n is the position
of the digit starting from 0 on the right.
Step 2: Add up all the resulting products. This sum gives you the decimal number.
Example: Convert (101001) to decimal number.
2
3
4
5
2
1
= 1 × 2 + 0 × 2 + 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 0
Sum of the products = 32 + 0 + 8 + 0 + 0 + 1 = 41
Therefore, (101001) = (41)
2 10
i + OPERATIONS ON BINARY NUMBERS
We can perform various operations on binary numbers. Let's discuss binary addition and binary
subtraction in detail.
Binary Addition
Binary addition is similar to the addition of decimal numbers. When the value of addition exceeds
the value 1, say 10 or 11, then 1 is carried over to the left of the current position.
The rules for adding two binary digits are given below:
X Y X + Y
0 0 0 + 0 = 0
0 1 0 + 1 = 1
1 0 1 + 0 = 1
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1 1 1 + 1 = 10 (carry 1) 1 1 1 1 1 Carry bits
1 0 1 1 1 1
For example, let us add the binary numbers (101111)
2
and (10111) . + 1 0 1 1 1
2
1 0 0 0 1 1 0
Binary Subtraction
In binary subtraction, the smaller binary number is subtracted from the larger one. The table
below illustrates how to subtract digit Y from digit X. If Y is greater than X, we borrow 1 from the
next higher position. When a binary digit of 0 borrows 1, it effectively becomes 2 (written as 10
in binary). The rules for binary subtraction:
25
Number System

