Thomas Tran
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Arithmetic & Memory
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Section Overview
In this section, we explore arithmetic operations and memory components - the building blocks that allow computers to perform calculations and store information. We’ll start with basic arithmetic circuits like adders, then move on to memory elements that can store and maintain state, and finally cover some advanced circuits that tie everything together.
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Arithmetic Operations
Double Trouble
This level has 4 inputs. Output is high when 2 or more of them are high.
View solutionMemory Components
Advanced Circuits
Arithmetic Operations
Double Trouble
At this level, we are tasked to create a circuit that outputs high if at least two inputs are on. This is also known as a majority logic circuit! These are commonly used for fault-tolerant systems or decision-making processes such as a voting system or controls!
Design Steps
- We use six AND gates to detect when each pair of inputs is high
- We use OR gates to combine the outputs of all pairs, so if any pair is high, the output is high.
- We connect the final OR gate to the output.
Odd Number of Signals
Here we want to use a maximum of 3 components to create an output where it is high only when an odd number of inputs are high. This is also known as a parity checker, commonly used for verifying data integrity in communication protocols or memory systems!
Design Steps
- We first connect inputs 1 and 2 to the first XOR gate. Then connect inputs 3 and 4 to the second XOR gate.
- We take the outputs of the first two XOR gates and connect them to a third XOR gate.
- This works because XOR gates can output high when an odd number of their inputs are high!
Memory Components
D-Latch
[Content for D-Latch…]
Advanced Circuits
Multiplexer
[Content for multiplexer…]