Binary Addition Rules (just like denary!):
0 + 0 = 0 (no carry) 0 + 1 = 1 (no carry) 1 + 0 = 1 (no carry) 1 + 1 = 10 (0 with carry 1) ← This is like 9+1=10 in denary! With carry from previous column: 1 + 1 + 1 (carry) = 11 (1 with carry 1)
Example 1: Simple Addition (no carry)
0011 (3)
+ 0101 (5)
------
1000 (8)
Check: 3 + 5 = 8 ✓
Example 2: Addition with Carry
0110 (6)
+ 0111 (7)
------
¹¹¹ ← carry bits
1101 (13)
Step-by-step:
Column 1 (rightmost): 0+1 = 1
Column 2: 1+1 = 0, carry 1
Column 3: 1+1+carry(1) = 1, carry 1
Column 4: 0+0+carry(1) = 1
Result: 1101 = 13 ✓
Example 3: Multiple Carries
10111 (23)
+ 01110 (14)
-------
¹¹ ¹ ← carry bits
100101 (37)
Check: 23 + 14 = 37 ✓
This key facts covers Binary Addition - The Foundation within Binary Arithmetic for GCSE Computer Science. Revise Binary Arithmetic in 3.3 Data Representation for GCSE Computer Science with 15 exam-style questions and 18 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 3 of 11 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Binary Arithmetic
In binary addition, what is the result of 1 + 1?
Explain the effect of a logical left shift and a logical right shift on the value of a binary number.