Integer representation and arithmetic pt2

Question 1

How does binary addition work (carrying and result)

Answer 1

• Add from least to most significant
• If 1 + 1 => carry 1 val 0
• If 1 + 1 + 1 (carry) => carry 1 val 1
• Carry is 1 larger than length

Question 2

What is the psuedo-code for addition in any base (digit by digit, low to high sig)

Answer 2

Question 3

What is a Full-Adder and its truth table

Answer 3

• Adds two single bits together

Question 4

How does a full-adder work in circuit

Answer 4

• Each full-adder is responsible for each bit (low to high signficance)

Question 5

What two cases can binary addition fail

Answer 5

1. The inputs are unsigned and there is a carry-out (larger than max val)
2. The inputs are signed but the sign of the result makes no sense (eg: 1000 0011 + 1000 0001 = 0000 0100, sign switch)

This problems can be detected and signaled to fix