This document explains binary number operations including addition, subtraction, multiplication, and division. It provides the rules and step-by-step workings for adding, subtracting, multiplying, and dividing binary numbers. Examples are shown of adding, subtracting, multiplying and dividing different binary numbers according to the rules provided.

1. NUMBER SYSTEM

2. BINARY ADDITION
Rules : 0+0 = 0
0+1 = 1
1+0 = 1
1+1 = 0,1 in
carry
For Example :
101
+101
1010
Q2. 101 + 101
1011
+1011
10110
Q3. 1011 + 1011
• To add these two numbers, we first consider the "ones" column and
calculate 1 + 1, which results in 10. We "carry" the 1 to the "tens"
column, and the leave the 0 in the "ones" column.
Q1. 100101 +
10101
100101
+10101
111010

3. Rules :
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 with a borrow of
1
Binary Subtraction
Q1. 101 from 1001
1 0 0 1
-1 0 1
1 0 0
Q2. 111 from 1000
1 0 0 0
- 1 1 1
0 0 0 1
Q3. 1 1 0 0 1 0 1 0 from 1 0 0 1 1 0
1 1
1 1 0 0 1 0 1 0
- 1 0 0 1 1 0 1 1
0 0 1 0 1 1 1 1
Q4. 1010101.10 from
1111011.11
1 1 1 1 0 1 1 . 1 1
-1 0 1 0 1 0 1 . 1 0
0 1 0 0 1 1 0 . 0 1
11010.101 from 101100.011
1 0 1 1 0 0 . 0 1 1
- 1 1 0 1 0 . 1 0 1
1 0 0 0 1 . 1 1 0

4. Binary Multiplication
Rules :
0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1
101
x11
101
101x
1111
11011
x101
11011
00000x
11011xx
1000111
Q1. 101 x 11 Q2. 11011 x 101

5. Q1. 11101.01 ÷ 1100
Solution:
1100) 11101.01 (10.0111
1100
10101
1100
0010
1100
1100
1100
Binary Division
Rules :
0/0 = Zero Error
0/1 = 0
1/0 = Zero Error
1/1 = 1
Q2. 10110.1 ÷ 1101
Solution:
1101) 10110.1 (1.101
1101
10011
1101
11000
1101
1011