Pt1420 Unit 6

1. Binary is just a different way of saying base 2. Thus, in binary, there are 2 symbols used to represent numbers: zero and one. In binary, we use powers of two. In the binary number 1001101, starting from the right being a base two power of zero, increasing the power by one each time the place is moved to the left, we get 87. The hexadecimal system is base 16. In hexadecimal, more symbols are needed after 10. Thus, in hexadecimal, the list of symbols is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. When you reach 9, you go directly to A. Then, you count B, C, D, E, and F. When we run out of symbols, a new digit placement is created and we move on.

2. Sometimes a very complex set of gates can be simplified to save on cost and make faster circuits. A way to do that is through boolean identities. Boolean identities are quick rules that allow you to simplify boolean expressions. To implement these identities, Boolean algebra is used.

3.

Two circuits are equivalent if they have the same characteristics at a specified pair of terminals. So circuit equivalency can be defined by, an electric circuit in a simple arrangement such that its performance would duplicate that of a more complicated circuit. By reducing the complicity of a circuit, this allows the circuit to be more efficient, which is beneficial.

4. Don’t cares in a truth table, are outputs the circuit produces that we quite literally don’t care about. They may be either 1s or 0s. They are helpful if they allow us to form a larger group than would otherwise be possible without the don’t cares. Only use don’t cares in a group if it simplifies the logic.

5. The goal of circuit minimization is to obtain the smallest circuit that represents a given Boolean formula or truth table. It is a logic optimization used to reduce the area of complex logic in integrated circuits, thus making the circuit more efficient, which is