Number systems Flashcards
How would one calculate the amount of different combinations of logic circuits with a specific base ?
in order to calculate this one needs to raise the base to the amount of circuits being used
What is sign and magnitude ? What are its problems ?
It is a way of expressing negative numbers in the binary system. It works by leaving the last digit to represent the sign as in 0 would indicate that the number is positive and 1 would indicate that the number is negative. The problems with the sign and magnitude solution is the fact that it complicates math operations as well as allowing for both negative and positive zero.
What are the benefits of the binary system ?
The benefits of the binary system
a) simplicity = the only two digits are 0 and 1
b) easier designing of logic circuits since binary system only has two discrete states
c) it takes less memory compared to other number system since it has only two discrete states
how would one calculate the amount of discrete states while knowing the amount of circuits and the base
one would need to multiply the base with the amount of circuits
Name different types of data which can be represented by the binary arrays?
numbers, symbols, logical variables, special characters
What are bits in the context of the digital system?
Bits are the smallest amount of data inside a digital system
Describe the 1s and 2s complement. What were the problems with the 1s complement ?
1s complement was the solution to the expression of negative numbers in the binary system. The way it works is by reversing each digit. For example 1000 would turn into 0111. Problems with the 1s complement was that it complicated the math operations as well as creating +0 and -0
2s complement is the current solution to expression of negative numbers in the binary system. It works by adding 1 to the 1s complement.
- it should also be noted that using this technique adds a extra number in a specific range
What is the difference between the positional and non-positional number system? And what are the problems with the non-positional system?
The difference between the positional and non-positional system is that in the non positional system the position of a digit does not affect the number while the opposite goes for the positional system
The problem with a non-positional system is that it requires frequent adding of new digits and it involves complex arithmatics
The positional number system works in a way where the value of each digit is defined by its position
What is the basic understanding of binary vectors and what is coding ?
Basic understanding of binary vectors is in the form of number
Coding is the act of assigning a meaning to the binary vector
Why is ternary theoretically the most optimal system ? And what are its problems ?
Following the math lead us to the conclusion that ternary is the most economical system since it strikes a perfect balance between the amount of available discrete states / digits and the amount of memory that it takes to express numbers
The problem with the ternary system is expensive production of hardware which would use the system as well as complex designing of logic circuits due to 3 discrete states
Describe how to represent the floating point numbers in the IEEE 754 standard
… check the presentation
How will the increase of the base affect the number of digits that is required to represent a specific number ?
Increasing the base will lead to fewer digits required to express a specific number
What is a format ?
Format is the way that a specific data type is written
- each data type is written in a specific format
how is data displayed inside a digital system?
Data inside a digital system is displayed in the form of binary vectors or bit arrays
What is a register ?
Register is a circuit which contains a series of numbers ready for arithmetic operations. It contains a fixed amount of latches or cells which limit the amount of digits that can be used in a given register.
