1. Binary Addition
CSC 103
September 17, 2007

2. Recap: Binary Numbers Physical representation Abstract representation
Transistor
Concept of “on” and “off” for physical manufacturing of computers  T/F…
Abstract representation
Logic: NOT, AND, OR
Truth tables
ANY Boolean expression can be built with transistors – wired as AND, OR or NOT

3. Recap: Transistors
= 0
= 1
= or = 1
= 1 or = 0
= 1

4. Logic Functions: NOT
The ‘NOT’ function
A A’
0 1
1 0

5. Recap Logic Gate: AND Function
(=1) 1
(=1) 1

6. Logic Gate: OR Function1 1 1 1

7. Onto Addition and
the Adder Circuit...

8. Binary Addition Add Add these numbers 1000111 1011010 0100110 0111001
0 + 0 =
0 + 1 =
1 + 0 =
1 + 1 =
Add these numbers c: s:

9. Binary Addition: Half Adder
We need a circuit to add two bits
Either bit can be ‘0’ or ‘1’
The function in the truth table is
Sum = A’B + AB’  Exclusive-OR function
Carry = AB

10. The Half-Adder and Exclusive OR Gate
A’B + AB’ = Exclusive OR
Typically abbreviated to XOR
Simulator uses EOR A B’ A’ B A B
A B | S C | | | |

11. Recap Logic Gates: Symbols
AB, AB A+B A, A’
XOR

12. Summary: The Half-Adder and Exclusive OR Gate
Typically abbreviated to XOR
Simulator uses EOR A B

13. Binary Addition: Half Adder

14. Half-Adder  Full-Adder

15. The Full Adder
A full adder is a circuit with three inputs (including a ‘carry-in’) and two outputs (the sum and carry-out)
What is the third input?
Exercise: Add
(carry)
( ‘A’ )
( ‘B’ )
(sum)
For adding two numbers, we need three inputs

16. The Full Adder
Cascade two half-adders to get a full adder A B
Cin

17. HW: Cascade 2 Full Adders for a 2-Bit Adder
A2A 
+ B2B 
B2 A B1 A1
Full Adder
Full Adder
Cout Cin2 = Cout Cin1
S S1

18. Summary Binary addition Concept of ‘sum’ and ‘carry’
Half adder and full adder circuits
Cascading circuits to make larger ones