Binary Arithmetic

Exam Tips - Binary Arithmetic

Most common exam questions:

• "Add these binary numbers" → Show carries, check your answer by converting to denary
• "What is overflow?" → Result too large for available bits, extra bits lost
• "Shift left by 2" → Multiplies by 4 (2²), add two 0s on right
• "Shift right by 1" → Divides by 2, add 0 on left, rightmost bit lost
• "Convert to two's complement" → Flip all bits, add 1

Binary addition tips:

• Work from RIGHT to LEFT (just like denary addition)
• Write carry bits above the calculation (small numbers)
• Remember: 1 + 1 = 0 with carry 1
• Always check your answer by converting to denary!

Shift operation tips:

• Left shift n places = multiply by 2ⁿ
• Right shift n places = divide by 2ⁿ
• Always fill with 0s (for unsigned numbers)
• Show the original and result clearly

Common mistakes to avoid:

• Forgetting to carry in binary addition
• Losing track of which direction to shift
• Saying "shift left divides" - NO! Left = multiply, right = divide
• Forgetting to add 1 after flipping bits in two's complement
• Not recognizing overflow when carry out of MSB