# How many values can be represented with 3 binary digits?

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 2^{3} 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 2^{0}x , the tens digit represents 2^{1}x, the hundredth base represents 2^{2}x, where x= 0 or 1.

Base2^{2}2^{1}2^{0}Values4 2 1 00 0 0 10 0 1 20 1 0 30 1 1 41 0 0 51 0 1 61 1 0 71 1 1

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.

Base2^{1}2^{0}Values2100 0 10 1 21 0 31 1

**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.

Base2^{3}2^{2}2^{1}2^{0}Values842100 0 0 0 10 0 0 1 20 0 1 0 30 0 1 1 40 1 0 0 50 1 0 1 60 1 1 0 70 1 1 1 81 0 0 0 91 0 0 1 101 0 1 0 111 0 1 1 121 1 0 0 131 1 0 1 141 1 1 0 151 1 1 1