Course
Packet
LM01-ICTCO
02C 0113
Learning Module
Computer Fundamental
Course Packet 2C
BINARY DIGITS
Knowledge Area Code
Course Code
Learning Module Code
Course Packet Code
:
:
:
:
ICT
ICTCO 113
LM-ICTCO113
LM-ICTCO-02C
Course Packet 02C
BINARY DIGITS
Introduction
The binary digit (shortened to “bit”) is the most elemental unit of information and in data communications
is represented as either a 1 or a 0. In and of itself, the single bit does not carry much information, but it
allows for very distinct states of being. For instance, a light is either on or off,
A binary digit, or bit, is the smallest unit of information in a computer. It is used for storing information
and has a value of true/false, or on/off. An individual bit has a value of either 0 or 1, which is generally
used to store data and implement instructions in groups of bytes.
Objectives
Understand that computers are digital devices so they use the binary number system
Be able to add, subtract, multiply and divide together two binary numbers
Learning Management System
https://www.khanacademy.org/computing/computers-and-internet/xcae6f4a7ff015e7d:digitalinformation/xcae6f4a7ff015e7d:binary-numbers/v/the-binary-number-system
Duration
 Topic 02C: Computer Hardware
( Binary Digits)
=
1 hour
(1 hour lecture/ activity)
Delivery Mode
Asynchronous ( Google Classroom)
Assessment with Rubrics
Requirement with Rubrics
Lesson Proper
A bit (short for binary digit) is the smallest unit of data in a computer. A bit has a single binary value, either
0 or 1. Although computers usually provide instructions that can test and manipulate bits, they generally
are designed to store data and execute instructions in bit multiples called bytes. In most computer systems,
there are eight bits in a byte. The value of a
bit is usually stored as either above or below a designated level of electrical charge in a single capacitor
within a memory device.
Half a byte (four bits) is called a nibble. In some systems, the term octet is used for an eight-bit unit
instead of byte. In many systems, four eight-bit bytes or octets form a 32-bit word. In such systems,
instruction lengths are sometimes expressed as full-word (32 bits in length) or half-word (16 bits in
length).
In telecommunication, the bit rate is the number of bits that are transmitted in a given time period,
usually a second.
Addition of Binary
Now that we know binary numbers, we will learn how to add them. Binary addition is much like your
normal everyday addition (decimal addition), except that it carries on a value of 2 instead of a value of 10.
For example: in decimal addition, if you add 8 + 2 you get ten, which you write as 10; in the sum this
gives a digit 0 and a carry of 1. Something similar happens in binary addition when you add 1 and 1; the
result is two (as always), but since two is written as 10 in binary, we get, after summing 1 + 1 in binary, a
digit 0 and a carry of 1.
Therefore in binary:
0+0=0
0+1=1
1+0=1
1 + 1 = 10 (which is 0 carry 1)
Example. Suppose we would like to add two binary numbers 10 and 11. We start from the last digit. Adding
0 and 1, we get 1 (no carry). That means the last digit of the answer will be one. Then we move one digit to
the left: adding 1 and 1 we get 10. Hence, the answer is 101. Note that binary 10 and 11 correspond to 2 and
3 respectively. And the binary sum 101 corresponds to decimal 5: is the binary addition corresponds to our
regular addition.
Rules of binary subtraction are as follows:
Binary Subtraction Table
0-0=0
1-0=1
1-1=0
0 - 1 = 1 with a borrow of 1
The rules of binary multiplication are given by
the following table:
×
1
0
1
1
0
0
0
0
As in decimal system, the multiplication of binary
numbers is carried out by multiplying the
multiplicand by one bit of the multiplier at a time
and the result of the partial product for each bit is
placed in such a manner that the LSB is under the
corresponding multiplier bit.
Finally the partial products are added to get the
complete product. The placement of the binary
point in the product of two binary numbers
having fractional representation is determined in
the same way as in the product of decimal
numbers with fractional representation. The total
number of places after the binary point in the
multiplicand and the multiplier is counted.
The method followed in binary division is also
similar to that adopted in decimal system.
However, in the case of binary numbers, the
operation is simpler because the quotient can
have either 1 or 0 depending upon the divisor.
The table for binary division is
- 1
0
-
0
1
0
0
1
1
1
0
1 1
Meaning less
0 0
Meaning less
The binary division operation is illustrated by
the following examples:
Evaluate:
(i) 11001 ÷ 101
solution:
101) 11001 (101
101
101
101
Hence the quotient is 101
(ii) 11101.01 ÷ 1100
Solution:
1100) 11101.01 (10.0111
1100
10101
1100
0010
1100
1100
1100
Hence the quotient is 10.0111
(iii) 10110.1 ÷ 1101
Solution:
1101) 10110.1 (1.101
1101
10011
1101
11000
1101
1011
Thus the quotient is 1.101 up to 3 places of
binary point and the remainder is 1.011.
(iv) 101.11 ÷ 111
Solution:
111) 101.11 (0.11
11 1
10 01
1 11
10
Thus the quotient is 0.11 up to 2 places of
binary point and the remainder is 0.1.
References
https://www.tutorialspoint.com/basics_of_computers/basics_of_computers_number_system_conversion.
htm
Activity Sheet
Do this : Include the computation.
No.
A
B
1
10100
11001
2
110
101
3
1010
1011
4
1100
1011
5
1100
1010
No.
A
B
1
110
101
2
1101
110
3
1100
110
4
1010
100
5
1111
100
Add
Subtract
.
Multiply
Divide
Assessment
Convert the following: Complete the table. Include the solution.
No
A
B
1
1000
1001
2
11001
10100
3
101000
101111
4
10101
10101
5
11111
11111
6
10000
11111
7
10100
10100
8
11100
10100
9
11100
10010
10
10100
10100
Add
Multiply
Assignment
1. What is Basic Logic Gates
2. List down different logic gates and its truth table.
3. Discuss the usage of logic gates.
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