binary addition
1. What Binary Addition Is
Binary addition = base-2 addition like decimal but with carry at 2 (since digit max 1). Rules:
i.e., sum bit = XOR, carry = AND.
2. Procedure (like decimal, carry to next higher bit)
Example: 1011 (11) + 0101 (5) = 10000? Let's add: 1011+0101=10000? Actually 11+5=16=10000₂ ✓
Column from LSB (right):
1+1=0 carry1
1+0+carry1=0 carry1
0+1+carry1=0 carry1
1+0+carry1=0 carry1 → new carry 1 ⇒ 10000
For more bits, propagate carry.
3. Worked Examples
(a) 1101 (13) + 1011 (11)= 11000? Actually 13+11=24=11000₂: 1101+1011=11000 (carry chain) ✓
(b) 1111+0001=10000 (15+1=16) ✓
(c) 1010.11 + 0111.01 =10010.00? 10.75+7.25=18.0=10010.0₂ ✓
(d) Hex addition similar but base16: 1A+2B=45₁₆? 1A+2B=26+43=69=45₁₆ ✓
(e) Overflow: 4-bit addition 1000+1000=0000 with carry out 1 (overflow if signed)
4. Exam Points
- State rules carry1 — 3-5 marks, very frequent (almost certain to ask addition).
- Add two 4-bit binaries with carry — 5-7 marks, very frequent (common numerical: add 1011+1010).
- Mention carry propagation — 3 marks.
- Show carry1 — 3 marks.