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How many values can be represented with 3 binary digits?

  • Last Updated : 05 Aug, 2021

The number system is a system of processing numbers. Number formats are the internal representation of numeric values in computer architecture. Numeric values are stored as groupings of bits, such as bytes and words. There are four different types of Number systems, the decimal system is mostly used, and the Binary system is used by computers. 

The four different types of number systems,

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1. Binary number system



This number system uses only two digits 0 and 1 followed with base 2. Binary digits also known as bits. Computers understand the Binary system only.

2. Octal number system

The octal number system referred to a base 8. It contains eight symbols.i.e;  0, 1, 2, 3, 4, 5, 6, 7.

3. Decimal number system

 It is the number system that uses digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 followed with base 10. In mathematics, decimal system is generally used.

4. Hexadecimal number system

Sixteen symbols used in hexadecimal system are 0,1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

A bit in Binary number



A single binary digit is called a bit. The binary number is made up of only 0’s and 1’s. These are the only two digits used and their combination in different ways is used to form different values/numbers. 

Example:

101 is a three-bit binary number

10100 is a five-bit binary number

How many values can be represented in 3 digit binary?

A three-digit binary simply means the arrangement of three 0’s and 1’s in all possible manners to form different values, for instance, 000, 001, 011, 100, etc. Since there are three digits, the maximum number of ways they can be arranged is 23 which is equal to 8. Hence, it gives numbers from 0-7. Below is the way to identify the number based on the three-digit binary, the unit digit represents 20x , the tens digit represents 21x, the hundredth base represents 22x, where x= 0 or 1.

Base222120
Values421
0000
1001
2010
3011
4100
5101
6110
7111

The maximum values represent in 3 digit binary is 0-7.

Similar Questions

Question 1: How many values can be represented using 2 digit binary?

Solution:

There are 4 values from 0-3 that can be represented using 2 digit binary.

Base2120
Values21
000
101
210
311

Question 2: How many values can be represented using 4 digit binary?

Solution:

There are 16 values from 0-15 that can be represented using 4 digit binary.

Base23222120
Values8421
00000
10001
20010
30011
40100
50101
60110
70111
81000
91001
101010
111011
121100
131101
141110
151111
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