Binary addition and two's complement: Class 11 practice
Binary addition uses 1 + 1 = 10 (write 0, carry 1). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Binary conversion
The idea behind binary addition and two's complement
Binary addition uses 1 + 1 = 10 (write 0, carry 1). Negative numbers are stored in two's complement: invert all bits of the positive value and add 1 (within a fixed number of bits).
Step-by-step method
- Line up the bits and add column by column with carries.
- For two's complement: write the 8-bit value, invert, add 1.
Worked example 1 (Basic)
Add (01101101)₂ and (00010000)₂.
- 109 + 16 = 125
- = (1111101)₂
- Answer: (1111101)₂
Worked example 2 (Standard)
Add (00111010)₂ and (00110011)₂.
- 58 + 51 = 109
- = (1101101)₂
- Answer: (1101101)₂
Worked example 3 (Challenge)
Write −100 in 8-bit two's complement.
- +100 = 01100100
- Invert: 10011011
- Add 1: 10011100
- Answer: 10011100
Common mistakes and misconceptions
- Forgetting the carry
- Adding 1 before inverting
Practice questions
- (Basic) Add (01001110)₂ and (01000001)₂.
- (Basic) Add (01001110)₂ and (01100101)₂.
- (Standard) Add (00011001)₂ and (01001110)₂.
- (Standard) Add (01110101)₂ and (00110011)₂.
- (Challenge) Write −98 in 8-bit two's complement.
- (Challenge) Write −23 in 8-bit two's complement.
Answer key with full working
- Q1: 78 + 65 = 143 → = (10001111)₂ → Answer: (10001111)₂
- Q2: 78 + 101 = 179 → = (10110011)₂ → Answer: (10110011)₂
- Q3: 25 + 78 = 103 → = (1100111)₂ → Answer: (1100111)₂
- Q4: 117 + 51 = 168 → = (10101000)₂ → Answer: (10101000)₂
- Q5: +98 = 01100010 → Invert: 10011101 → Add 1: 10011110 → Answer: 10011110
- Q6: +23 = 00010111 → Invert: 11101000 → Add 1: 11101001 → Answer: 11101001
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 addition and two's complement 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.