# Computer Architecture

4.3 Adders Page 4.2 First, we will need the following:
x ( y ( z is 1 when just one or all three of x, y, z, is 1.
xy + xz + yz = xy ( xz ( yz, and is 1 when at least two of x, y, z, is 1. Half adder:
Symbol Function Truth table Outputs Circuit _____ x ___ c |x c| s = arith x + y x y s d s = x ( y ------*-------|AND|------- | HA | with carry out c 0 0 0 0 c = xy -------|---*---|___| |y s| 0 1 1 0 y | | ___ s |_____| 1 0 1 0 | |---|XOR|------- 1 1 0 1 |-------|___|

Symbol Function Truth table Outputs
_____
|c d| s = arith x + y x y c s d s = x ( y ( c
| | with carry in c 0 0 0 0 0 d = xy ( xc ( yc |x | and carry out d 0 0 1 1 0
| FA | 0 1 0 1 0 noting s = 1 when 1 or all 3 of x,y,c = 1 |y s| 0 1 1 0 1 d = 1 when at least 2 of x,y,c = 1 |_____| 1 0 0 1 0

1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
Circuit
x ____ xy _____ d = xy ( xc ( yc ----------|x c|-----------------------------------| |---------------------- | HA | ____ | XOR |

----------|y s|--------|x c|---------------------|____ |
y |____| x ( y | HA | c(x ( y) = cx ( cy
| |
------------------------|y s|------------------------------------------------ c |____| s = x ( y ( c There is a "handle cranking" way of getting an expression for d. _...