The document discusses the decimal and binary number systems. It explains that computers use binary, which represents numbers as sequences of 0s and 1s, because their internal workings are based on two states of electricity - on or off. It then shows how to convert between decimal and binary, and how to perform arithmetic operations like addition, subtraction, multiplication and division in binary. Some examples of these binary operations are provided. Finally, it gives some practice problems to convert between decimal and binary, and perform binary arithmetic.

1. THE NUMBER SYSTEM
Decimal Number System and
Binary Number System

2. The number system that we use in
expressing numerical values. It is a
base 10 number system wherein
the numbers are expressed in
scale of tens.

4. 

Computer work on electrical pulses
with only 2 state, “on” or “off”

5. 

6.  DIVISION QUOTIENTS REMAINDERS
13/2 6 1
6/2 3 0
3/2 1 1
1/2 0 1
Therefore 13=1101

7. 

8. To covert the binary digits 1011 back
to its decimal form, the following
method is performed:
1 x 2 = 2
2 + 1 x 2 = 6
6 + 0 x 2 = 12
12 + 1 = 13

9. ARITHMETIC OPERATIONS WITH BINARY
NUMBERS
Binary Addition
Binary Subtraction
Binary Multiplication
Binary Division

10. BINARY ADDITION

12. BINARY SUBTRACTION

13. Examples:
A. 1010 B. 1111
- 100 - 1000
110 111
To subtract, it is necessary to establish a
procedure for subtracting a larger from smaller
digit. The only case in which this occur using
binary number is when 1 is subtracted from 0.
The remainder is 1, but it is necessary to
borrow 1 from the next column to the left.

14. As, in decimal multiplication, we
shift one place to the left after
obtaining each partial product, and
in the end add up all the partial
products, and in the end add up all
the partial products to obtain the
answer.
BINARY MULTIPLICATION

16. BINARY MULTIPLICATION

17. In the decimal system, division is the
inverse of multiplication and division
by zero is similarly meaningless.
Division is defined as the process of
determining how many times one
number, the divisor, can be subtracted
from one another number, the
dividend, while still leaving a positive
remainder. The number of times this
can be done is the result, or quotient.

18. 0/1 = 0
1/1 = 1

19. 1. Add the following unsigned binary numbers:
A. 00101011 B.01100001 C. 01000010
01111111 01111111 01001100
D. 00001111 E. 01010101
00000001 00000010
2. Convert the following binary numbers to decimal
value:
A. 01101111 B. 00011000
C. 00110101 D. 01011011 E. 01011000
LETS CHECK!

20. The complete table for binary division is
11
Example: 100 1100
100___
100
100
000

21. 3. Compute 01101010 x 111. Show your
work.
4. Divide 01011 into 011011000. Show your
work.
5. Convert 137 and 42 to binary. Compute
the binary equivalent of 137 - 42. Show
your solution.
6. Compute 52 – 22 in binary. Show your
solution.

22. 1. Perform the following task. Show your solution on
your notebook.
 Convert the following binary numbers to
decimal.
a) 0001 1001
b) 1111 1101
c) 0010 1001 1000
b) 1101 0101
c) 0011 1010
d) 1110 1110 1110

23. Convert the following decimal numbers
to binary.
A) 29
B) 250
C) 1000
D) 78
E) 315
F) 2049

24. 2. Make a research about the following:
a. ASCII CODE
b. Binary Arithmetic