1. ECE 3110: Introduction to Digital Systems
Number Systems: unsigned numbers addition/subtraction

2. Previous class Summary
Conversions:
Binary, Oct, Hex
Any number <---->Decimal

3. Binary Addition, Subtraction (single digit)
The rules for binary addition are:
The rules for binary subtraction are:
0 + 0 = 0, carry = 0
0 - 0 = 0, borrow = 0
1 + 0 = 1, carry = 0
1 - 0 = 1, borrow = 0
0 + 1 = 1, carry = 0
0 - 1 = 1, borrow = 1
1 + 1 = 0, carry = 1
1 - 1 = 0, borrow = 0
Multiple digits:
Borrows, Carries from digits to left of current of digit.
Binary subtraction, addition works just the same as decimal addition, subtraction.

4. Binary Addition, Subtraction (multiple digits)
cin or bin X Y
Cout s
Bout d 1

5. Binary, Decimal addition
From LSB to MSB: 1+1 = 0, carry of 1 1 (carry)+1+0 = 0, carry of 1 1 (carry) = 1, no carry = = = 1 answer = 34
from LSD to MSD: 7+4 = 1; with carry out of 1 to next column
1 (carry) = 5. answer = 51.

6. Subtraction Binary Decimal 900 1002
= 9; with borrow of 1 from next column 0 -1 (borrow) - 0 = 9, with borrow of (borrow) - 0 = 8. Answer = 899.
1002
= 1; with borrow of 1 from next column 0 -1 (borrow) - 0 = 1, with borrow of (borrow) - 0 = 0. Answer = 0112.

7. Octal/Hex addition/subtraction
Rarely
Convert to decimal-->calculate results-->convert back.
Column addition/subtraction (example pp34)

8. Next…
Signed numbers