Computer Systems 2.1&2.2

Notes for lectures 2.1 and 1.2

What is the result of 1 + 1 + 1 in binary?

1 with a carry of 1.

What is the result of 0 - 1 in binary?

1 with a borrow of 1.

In the Sign and Magnitude method, what is the role of the Most Significant Bit (MSB)?

It acts as the sign bit: 0 for positive (+), and 1 for negative (-).

What is the primary limitation of the Sign and Magnitude method?

It results in two different representations for the number zero (positive zero and negative zero).

How do you calculate the 1's Complement of a binary number?

Invert every single bit (0 becomes 1, and 1 becomes 0).

How do you calculate the 2's Complement of a binary number?

Find the 1's Complement and then add 1 to the result.

What is the main operational advantage of using 2's Complement?

It allows subtraction operations to be performed using simple addition, which simplifies computer hardware design.

In 2's Complement subtraction, if a final carry is generated, what does that indicate about the result?

The result is positive, and the final carry should be disregarded.

What fundamental electronic device acts as an ON/OFF switch in digital logic circuits?

The Transistor.

What is the primary function of a Logic Gate?

To perform logical operations on one or more binary inputs to produce a single binary output

What determines the output of a Logic Gate for every possible input combination?

The Truth Table

Which type of logic gate has an output of 1 only when all of its inputs are 1?

The AND gate

Which gate is the only one that can have only one input?

The NOT gate (Inverter)

What is the condition for an XOR gate to produce an output of 1?

The inputs must be different.

Which two gates are considered universal gates because they are AND or OR gates followed by a NOT gate?

NAND (NOT AND) and NOR (NOT OR)

For a circuit with 5 inputs, how many rows would its truth table have?

32 rows (2 to the power of 5)