Binary ↔ decimal conversion: Class 11 practice
In binary each place is a power of 2. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Powers of 2
The idea behind binary ↔ decimal conversion
In binary each place is a power of 2. To convert binary to decimal, add the place values of the 1s. To convert decimal to binary, divide by 2 repeatedly and read the remainders from bottom to top.
Step-by-step method
- Binary → decimal: sum 2ⁿ for each 1 bit.
- Decimal → binary: repeated division by 2.
- Read remainders upwards.
Worked example 1 (Basic)
Convert 30 to binary.
- Repeated division by 2, remainders read upwards
- = (11110)₂
- Answer: (11110)₂
Worked example 2 (Standard)
Convert (10111111)₂ to decimal.
- 2^7 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0
- = 191
- Answer: 191
Worked example 3 (Challenge)
Convert 185 to binary.
- Repeated division by 2, remainders read upwards
- = (10111001)₂
- Answer: (10111001)₂
Common mistakes and misconceptions
- Reading remainders top-down
- Starting place values at 2¹
Practice questions
- (Basic) Convert 29 to binary.
- (Basic) Convert 26 to binary.
- (Standard) Convert (11101111)₂ to decimal.
- (Standard) Convert (10000111)₂ to decimal.
- (Challenge) Convert 261 to binary.
- (Challenge) Convert 353 to binary.
Answer key with full working
- Q1: Repeated division by 2, remainders read upwards → = (11101)₂ → Answer: (11101)₂
- Q2: Repeated division by 2, remainders read upwards → = (11010)₂ → Answer: (11010)₂
- Q3: 2^7 + 2^6 + 2^5 + 2^3 + 2^2 + 2^1 + 2^0 → = 239 → Answer: 239
- Q4: 2^7 + 2^2 + 2^1 + 2^0 → = 135 → Answer: 135
- Q5: Repeated division by 2, remainders read upwards → = (100000101)₂ → Answer: (100000101)₂
- Q6: Repeated division by 2, remainders read upwards → = (101100001)₂ → Answer: (101100001)₂
Syllabus note
This skill is listed under "Computer Systems and Organisation" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is binary ↔ decimal conversion in?
"Computer Systems and Organisation", Class 11 Computer Science (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.