Number System and Binary Conversion Notes for SSC Exams

Number system in computers is a scoring topic of SSC Computer Knowledge. A computer understands only 0s and 1s, so the questions are on the binary, octal and hexadecimal systems and simple conversions. These computer number system notes for SSC explain the methods with solved examples. Read it with the Computer Memory Notes and Logic Gates and Boolean Algebra Notes notes.

Types of Number Systems

System	Base	Digits used
Binary	2	0, 1
Octal	8	0 to 7
Decimal	10	0 to 9
Hexadecimal	16	0 to 9 and A to F (A = 10, B = 11, C = 12, D = 13, E = 14, F = 15)

Computers use the binary system because electronic circuits have two states: ON (1) and OFF (0).

Binary to Decimal

Multiply each digit by a power of 2, starting from 2 raised to 0 on the right, and add them. For binary 1011: 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1 = 11.

Decimal to Binary

Divide the number by 2 repeatedly and write the remainders from the bottom to the top. For decimal 13: 13 / 2 = 6 remainder 1; 6 / 2 = 3 remainder 0; 3 / 2 = 1 remainder 1; 1 / 2 = 0 remainder 1. Reading from the bottom: 1101.

Useful Binary Values

Decimal	Binary	Decimal	Binary
1	1	6	110
2	10	7	111
3	11	8	1000
4	100	9	1001
5	101	10	1010

Octal and Hexadecimal Shortcuts

• To convert binary to octal, group the bits in threes from the right: 101110 = 101 and 110 = 56 (octal).
• To convert binary to hexadecimal, group the bits in fours from the right: 11010110 = 1101 and 0110 = D6.
• Hexadecimal is commonly used for colour codes and memory addresses.
• Decimal 255 = binary 11111111 = hexadecimal FF.

Character Codes and Binary Arithmetic

• ASCII (American Standard Code for Information Interchange) uses 7 bits (128 characters); extended ASCII uses 8 bits (256 characters).
• Unicode supports characters of all world languages (16 bits or more).
• BCD (Binary Coded Decimal) uses 4 bits for each decimal digit.
• Binary addition rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1 and 1 + 1 = 10 (0 carry 1).
• The ASCII value of A is 65, a is 97 and 0 is 48.

Place Value in Different Number Systems

System	Place values from the right
Decimal	1, 10, 100, 1000 (powers of 10)
Binary	1, 2, 4, 8, 16, 32, 64, 128 (powers of 2)
Octal	1, 8, 64, 512 (powers of 8)
Hexadecimal	1, 16, 256, 4096 (powers of 16)

To convert any number into decimal, multiply each digit by its place value and add the results. This is the method used in binary to decimal, octal to decimal and hexadecimal to decimal conversions.

Conversion Table for 0 to 15

Decimal	Binary	Octal	Hexadecimal
0	0000	0	0
1	0001	1	1
2	0010	2	2
3	0011	3	3
4	0100	4	4
5	0101	5	5
6	0110	6	6
7	0111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
12	1100	14	C
13	1101	15	D
14	1110	16	E
15	1111	17	F

More Solved Conversions

• Decimal 25 to binary: 25 / 2 = 12 r 1; 12 / 2 = 6 r 0; 6 / 2 = 3 r 0; 3 / 2 = 1 r 1; 1 / 2 = 0 r 1. Reading upwards: 11001.
• Binary 11001 to decimal: 16 + 8 + 0 + 0 + 1 = 25.
• Decimal 100 to hexadecimal: 100 / 16 = 6 r 4, so 64 in hexadecimal.
• Hexadecimal 2F to decimal: 2 x 16 + 15 = 47.
• Octal 17 to decimal: 1 x 8 + 7 = 15.
• Binary 1101 0110 to hexadecimal: 1101 = D and 0110 = 6, so D6.
• Octal 57 to binary: 5 = 101 and 7 = 111, so 101111.

Binary Arithmetic

Operation	Rules
Addition	0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; 1 + 1 = 10 (write 0, carry 1); 1 + 1 + 1 = 11
Subtraction	0 - 0 = 0; 1 - 0 = 1; 1 - 1 = 0; 0 - 1 = 1 with a borrow
Multiplication	0 x 0 = 0; 0 x 1 = 0; 1 x 1 = 1
Division	Done like decimal long division with binary numbers

Example: 1011 + 0110. Add from the right: 1 + 0 = 1; 1 + 1 = 0 carry 1; 0 + 1 + 1 = 0 carry 1; 1 + 0 + 1 = 0 carry 1; the last carry gives 1. The result is 10001 (11 + 6 = 17).

Complements and Negative Numbers

• 1's complement of a binary number is found by changing every 0 to 1 and every 1 to 0.
• 2's complement is the 1's complement plus 1. Computers use it to show negative numbers and to do subtraction.
• In signed numbers, the leftmost bit is the sign bit: 0 means positive and 1 means negative.
• Fractions use a binary point: 0.1 in binary = 0.5 in decimal.

Character Codes and Data Representation

Code	Details
ASCII	7 bits (128 characters); A = 65, a = 97, 0 = 48
Extended ASCII	8 bits (256 characters)
EBCDIC	8-bit code used in IBM mainframes
Unicode	Supports all languages; UTF-8 uses 1 to 4 bytes per character
BCD	4 bits for each decimal digit
Gray code	Only one bit changes between two consecutive numbers

• A bit is the smallest unit of data; a byte is 8 bits and holds one character.
• A word is the amount of data processed by the CPU at one time (32-bit or 64-bit).
• Parity bit is an extra bit added to detect errors in the data.
• Boolean logic uses true (1) and false (0) with the AND, OR and NOT operations.

Important Questions Explained

Question 1: Convert binary 1011 into decimal.
Answer: 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1 = 8 + 0 + 2 + 1 = 11.

Question 2: Convert decimal 13 into binary.
Answer: Dividing by 2 gives remainders 1, 0, 1, 1 from the bottom to the top, so 13 = 1101.

Question 3: What is the base of the hexadecimal system?
Answer: 16.

Question 4: What is the hexadecimal value of decimal 255?
Answer: FF.

Question 5: How many characters can ASCII (7-bit) represent?
Answer: 128 characters.

Question 6: What does 1 + 1 equal in binary?
Answer: 10 (zero with a carry of one).

Quick Tips to Remember

• Learn the powers of 2: 1, 2, 4, 8, 16, 32, 64, 128 and 256.
• For binary to octal use groups of 3 and for hexadecimal use groups of 4.
• Remember A to F as 10 to 15.
• Remember the ASCII values: A = 65, a = 97 and 0 = 48.
• Check the answer by converting it back.

Common Mistakes to Avoid

• Writing the remainders from the top to the bottom in decimal to binary.
• Mixing the base of octal (8) and hexadecimal (16).
• Using the digits 8 and 9 in the octal system.
• Confusing ASCII (7 bits) with extended ASCII (8 bits).
• Forgetting the carry in binary addition.

Quick Revision Points

• Binary base 2, octal base 8, decimal base 10, hexadecimal base 16.
• Decimal to binary: divide by 2 and read remainders bottom to top.
• Binary to octal: groups of 3; to hex: groups of 4.
• ASCII = 7 bits; Unicode covers all languages.
• 1 + 1 = 10 in binary.

Practice Questions With Answers

1. What is the base of the binary system?
   Answer: 2 (Digits 0 and 1).
2. Convert 101 (binary) to decimal.
   Answer: 5 (4 + 0 + 1).
3. Convert 10 (decimal) to binary.
   Answer: 1010 (8 + 2).
4. What is the base of the octal system?
   Answer: 8 (Digits 0 to 7).
5. Which letters are used in hexadecimal?
   Answer: A to F (A = 10, F = 15).
6. How many bits are in a byte?
   Answer: 8 (Memory unit).
7. What does ASCII stand for?
   Answer: American Standard Code for Information Interchange (7-bit code).
8. Which code supports all world languages?
   Answer: Unicode (16 bits or more).
9. What is hexadecimal F in decimal?
   Answer: 15 (Highest single digit).
10. What is binary 111 in decimal?
    Answer: 7 (4 + 2 + 1).

More Practice Questions With Answers

1. What is decimal 25 in binary?
   Answer: 11001 (Divide by 2).
2. What is binary 11001 in decimal?
   Answer: 25 (16 + 8 + 1).
3. What is decimal 100 in hexadecimal?
   Answer: 64 (100 / 16).
4. What is hexadecimal 2F in decimal?
   Answer: 47 (2 x 16 + 15).
5. What is the 1's complement of 1010?
   Answer: 0101 (Flip the bits).
6. What is the 2's complement used for?
   Answer: Showing negative numbers (Subtraction).
7. What is binary 1111 in octal?
   Answer: 17 (Groups of 3).
8. What does a sign bit 1 mean?
   Answer: Negative number (Leftmost bit).
9. How many characters can extended ASCII show?
   Answer: 256 (8 bits).
10. What does parity bit do?
    Answer: Detects errors (Error checking).
11. What is binary 1011 + 0110?
    Answer: 10001 (11 + 6 = 17).
12. What is the ASCII value of A?
    Answer: 65 (a = 97).

How to Practise This Chapter

1. Read the tables once and learn the key facts by heart.
2. Revise the quick revision points the next day.
3. Attempt the practice questions above without looking at the answers.
4. Solve a full SSC CGL Tier 1 mini mock to test your general awareness.
5. Check the previous year papers to see how SSC asks computer questions.

Related Notes and Practice Papers

• Computer Memory Notes
• Logic Gates and Boolean Algebra Notes
• Computer Languages and Translators Notes
• Computer Knowledge Notes for SSC
• SSC CGL Tier 1 Mini Mock

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• General Science Notes
• General Awareness Notes
• Quantitative Aptitude Notes
• Reasoning Notes
• Electrical Engineering (SSC JE) Notes
• All SSC subjects and notes

Frequently Asked Questions

Why do computers use the binary system?

Computers use binary because electronic circuits have two states, ON and OFF, which are shown as 1 and 0.

What is the base of a number system?

The base is the number of digits used in the system, such as 2 for binary and 10 for decimal.

How do I convert decimal to binary?

Divide the number by 2 again and again, and write the remainders from the bottom to the top.

How do I convert binary to decimal?

Multiply each bit by the power of 2 for its place and add the results.

What are the digits of the hexadecimal system?

The digits are 0 to 9 and the letters A to F.

What is ASCII?

ASCII is a code in which each character is given a number, using 7 bits for 128 characters.

What is Unicode?

Unicode is a standard that gives a number to the characters of all world languages.

What is BCD?

BCD means Binary Coded Decimal, in which each decimal digit is written in 4 bits.

How many questions come from number system in SSC exams?

One question usually comes on the number system and binary conversion.

What is the 2's complement?

The 2's complement is found by taking the 1's complement of a binary number and adding 1. It is used to show negative numbers.

What is a parity bit?

A parity bit is an extra bit added to the data to detect errors during transmission.

What is the difference between ASCII and Unicode?

ASCII uses 7 bits and covers 128 characters mostly of English, while Unicode covers the characters of all the world languages.