Arithmetic Microoperations

1
Arithmetic Microoperations
Addition
Subtraction
1s Complement
2s Complement
Subtraction!
Increment
Decrement
2
Full Adders and Half Adders
3
Full Adders and Half Adders
Ai Bi Si Ci 0 0 0 0 0 1 1 0 1 0
1 0 1 1 0 1
Ai Bi
HA
Ci Si
4
An n-bit adder
An-1 Bn-1 Cn-2
...
FA
Cn-1 Sn-1
5
Another n-bit adder
0 v
6
An n-bit incrementer
5 v
An-1 Bn-1
...
HA
Cn-1 Sn-1
7
Block Diagrams
How many pins in this chip?
2n A,B 1 CIN n Sum 1 COUT 1 Clock
1 VCC 1 Gnd 3n5
n-bit adder
An-1 Bn-1 ...A1 B1 A0 B0 CIN
COUT Sn-1 Sn-2 S1 S0
How many inputs? How many outputs?
2n1
n1
8
Inside the n-bit clocked adder
...
FA
FA
FA
FA
n-bit register
9
Subtraction

• A- B A 2s complement of B
• 2s complement of B B 1
• B B ? 1 B exclusive OR 1 where 1 is n
  1s

X Y X ?Y 0 0 0 0 1 1 1 0 1 1 1 0