Full Adder
ucla | CS M51A | 2023-01-10T14:35
Table of Contents
Definitions
- prime
- when the incoming bit is 0, denote its variable with a prime
- e.g. Xi’ denotes 0 bit while Xi denotes 1 bit
Big Ideas
Logic Gates
 |
NOT Gate
- inverter, ON only when input is bit 0
| in | out |
| 0 | 1 |
| 1 | 0 |
Full Adder
- sum of products
$Zi = X_i’Y_i’C_{in} + X_i’Y_iC_{in}’ + X_iY_i’C_{in}’ + X_iY_iC_{in}$
- product of sums
$Z_i = (X_i+Y_i+C_{in})(X_i+Y_i’+C_{in}’)(X_i’+Y_i+C_{in}’)(X_i’+Y_i’+C_{in})$
- singular addition unit with a carry forward capability and 2 parameters
- can be placed in series to carry forward addition parameters and carry bits
truth table
- equations can be written as:
- $Zi=(Xi+Yi+Ci)…(Xi’+Yi’+Ci’)$
Resources
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**SUMMARY
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