Computer systems 3.1&3.2

Notes for lectures 3.1&3.2

What is the main practical benefit of simplifying a Boolean expression?

It reduces the complexity of the digital circuit by using fewer logic gates, resulting in an optimized circuit

According to the Complement Law, what is the result of a variable ORed with its NOT?

1 (X OR NOT X = 1)

Which Boolean Law states that NOT (NOT X) = X?

The Involution Law

Which theorem allows you to change a NOT AND operation into a NOT OR operation, and vice versa?

De Morgan's Theorem

What is the first step when deriving a Boolean equation from a logic circuit?

Start from the leftmost inputs and work toward the final output.

When deriving an equation from a truth table, when should you use the rows with '0' outputs and then invert the result?

In Case 3, when there are more '1' outputs than '0' outputs.

What is the basic function of a Decoder?

To detect a specific combination of bits on its n inputs and select one of its up to 2^n outputs

What is an Encoder in relation to a decoder?

An encoder is essentially the reverse of a decoder circuit, accepting many inputs and producing a coded, fewer number of outputs

What is the fundamental difference between a Combinational Circuit and a Sequential Circuit?

Combinational output depends on current inputs only. Sequential output depends on current inputs and the previous state (memory).

What is the simplest electronic storage device that can hold one bit of information?

A Latch.

What is the primary characteristic of a Flip-Flop compared to a Latch?

Flip-Flops are synchronous, meaning their state change is controlled by a clock signal.

Which type of flip-flop is commonly used to construct Registers?

The D Flip-Flop (Data/Delay).

How is a Register constructed, and what is its role in the CPU?

It is a group of D Flip-Flops used for temporary storage and manipulation of data words in the CPU

What type of flip-flop is commonly used to build a Counter?

The T Flip-Flop (Toggle).

What is the function of a Shift Register?

To store data and shift the stored data left or right on each clock cycle, facilitating serial-to-parallel or parallel-to-serial conversion.

In an Asynchronous (Ripple) Counter, what is the clock input for a flip-flop?

The output of the preceding flip-flop in the chain.