HW 4

Question 1

Explain the procedure for adding two numbers in 1’s complement form.

Answer 1

1. Add the two binary numbers bit by bit.
2. If there’s a carry out from the most significant bit (MSB), add this carry back to the least significant bit (LSB) — called end-around carry.
3. If no carry, result is the sum.
4. Check sign:

If result is all zeros, it’s zero.

Otherwise, result is in 1’s complement form.

Question 2

How do you identify an overflow condition when you add two numbers in 1’s complement form? Provide an example for this.

Answer 2

Identification:
Overflow occurs if adding two numbers with the same sign produces a result with a different sign.

Example:
Add +3 (0011) and +4 (0100) in 4-bit 1’s complement:
Answer: -6, Overflow (sign changed from + to - )

Question 3

What does BCD stand for?

Answer 3

Binary Coded Decimal

Question 4

Explain at least two important disadvantages of storing numbers in BCD format.

Answer 4

1. Inefficient Storage:
   BCD uses 4 bits to store each decimal digit (0–9), wasting space since 4 bits can represent 16 values (0–15), but only 10 are used.
2. Slower Processing:
   Arithmetic operations (like addition and subtraction) are more complex and slower compared to pure binary, requiring extra correction steps.

Question 5

Offer one advantage for using a BCD format for storing numbers.

Answer 5

Easy Decimal Conversion:
BCD makes it simple to convert between binary and decimal, making it ideal for financial and digital display systems (e.g., calculators, digital clocks).