# What does the binary number 0111 represent?

A Number System is a way of Representing Numbers. Representation of Numbers is done by using digits or symbols. The Numbers that are represented by digits or symbols have the value and the value depends on the place, base, and value of the digits used. There are 4 different types of Number Systems, which define different Base Numbers. They are:

- Binary Number System
- Octal Number System
- Hexadecimal Number system.
- Decimal Number System.

All these Number Systems have different bases. The Numbers in each system are represented with their bases which are raised to the power of their position from rightmost as 0 and the left of it as 1. These are multiplied with the Numbers at each position and the cumulative sum of all these gives the value.

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Positions of each digit:for Decimal Number 38479 is

Digits: 3 8 4 7 9

Positions: 4 3 2 1 0

Each digit is multiplied by 10^{(Position of each digit)}

### Decimal Number System

A Decimal Number System is the System in which the Numbers are represented by digits from (0- 9). A Number in Octal Number System is represented by Base 8 and the Binary number system is represented by base 2. Any Number of Decimal System can be represented in (0-9) in Decimal System.

**For Example **Decimal Number representation from 0 to 10

0 ⇢ 0( 0×10

^{0})1 ⇢ 1( 1×10

^{0})2 ⇢ 2( 2×10

^{0})3 ⇢ 3( 3×10

^{0})4 ⇢ 4( 4×10

^{0})5 ⇢ 5( 5×10

^{0})6 ⇢ 6( 6×10

^{0})7 ⇢ 7( 7×10

^{0})8 ⇢ 8( 8×10

^{0})9 ⇢ 9( 9×10

^{0})10 ⇢ 10( 1×10

^{1 }+ 0×10^{0})

**Octal Number System**

An Octal Number System is the System in which the Numbers are represented by digits from (0 – 7). A Number in Octal Number System is represented by Base 8. Any Number of Decimal Systems can be represented in (0- 7) in Octal System.

**For Example **Octal Number representation in Binary Number System. (from 0 to 10 of Decimal Numbers to Octal Numbers)

Decimal – Octal0 ⇢ 0( 0× 8

^{0})1 ⇢ 1( 1× 8

^{0})2 ⇢ 2( 2× 8

^{0})3 ⇢ 3( 3× 8

^{0})4 ⇢ 4( 4× 8

^{0})5 ⇢ 5( 5× 8

^{0})6 ⇢ 6( 6× 8

^{0})7 ⇢ 7( 7× 8

^{0})8 ⇢ 10( 1× 8

^{1}+ 0× 8^{0})9 ⇢ 11( 1× 8

^{1}+ 1× 8^{0})10 ⇢ 12( 1×8

^{1 }+ 2×8^{0})

**Hexadecimal Number System**

A Hexadecimal Number System is a System in which the Numbers are represented by digits from (0 – 9) and (A-F). A Number in Hexadecimal Number System is represented by Base 16. Any Number of Decimal Systems can be represented by (0 – 9) and (A-F) in Hexadecimal System.

**For Example** Hexadecimal Number representation in Binary Number System. (from 0 to 15 of Decimal Numbers to Hexadecimal Numbers)

Decimal ⇢ Hexadecimal0 ⇢ 0

1 ⇢ 1

2 ⇢ 2

3 ⇢ 3

4 ⇢ 4

5 ⇢ 5

6 ⇢ 6

7 ⇢ 7

8 ⇢ 8

9 ⇢ 9

10 ⇢ A

11 ⇢ B

12 ⇢ C

13 ⇢ D

14 ⇢ E

15 ⇢ F

### Binary Number System

A Binary Number System is a System in which the Numbers are represented in 0s and 1s. A Number in Binary Number System is represented by Base 2. Any Number of Decimal Systems can be represented in 0s and 1s in Binary System.

**For Example** Decimal Number representation in Binary Number System.(from 0 to 10 of Decimal Numbers to Binary Numbers)

Decimal ⇢ Binary0 ⇢ 0

1 ⇢ 1

2 ⇢ 10

3 ⇢ 11

4 ⇢ 100

5 ⇢ 101

6 ⇢ 110

7 ⇢ 111

8 ⇢ 1000

9 ⇢ 1001

10 ⇢ 1010

### What does 0111 mean in Binary?

A Binary Number is a number that is expressed in a binary numeral system. Any Number can be Expressed in Binary ie., in 0s and 1s. Each digit that is either 0 or 1 in a Binary Number is called a **Bit. **In Binary, the Rightmost Bit is the 0th Bit, and the Bit before that is the 1st Bit, and so on.

A Binary Number can be Converted into a Decimal Number by the Addition of the Bit multiplied with 2 raised to the Power of position of the Bit.

1 ⇢ 0th bit

1 ⇢ 1st bit

1 ⇢ 2nd bit

0 ⇢ 3rd bit

the Decimal Number can be Obtained as ((2

^{3})× 0)+ (2^{2})× 1)+ (2^{1})× 1)+ (2^{0})× 1)) = ((8×0) + (4×1) + (2×1) + (1×1)) = 0+ 4+ 2+1= 7

0111 in binary is 7 in Decimal

**Similar Questions**

**Question 1: 11111 in Binary to Decimal is?**

**Solution:**

1 ⇢ 0th bit

1 ⇢ 1st bit

1 ⇢ 2nd bit

1 ⇢ 3rd bit

1 ⇢ 4th bit

The Decimal Number can be Obtained as ((2

^{4})×1)+ (2^{3})× 1)+ (2^{2})× 1)+ (2^{1})× 1)+ (2^{0})× 1)) = ((16× 1)+ (8× 1)+ (4× 1) + (2×1) + (1×1)) = 16+ 8+ 4+ 2+ 1 = 31

11111 in binary is 31 in Decimal

**Question 2: Convert 01010 (binary) to decimal.**

**Solution:**

0 ⇢ 0th bit

1 ⇢ 1st bit

0 ⇢ 2nd bit

1 ⇢ 3rd bit

0 ⇢ 4th bit

The decimal form is,

0× 2

^{4}+ 1× 2^{3}+ 0× 2^{2}+ 1× 2^{1}+ 0× 2^{0}8+ 2= 10

01010 is 10 in Decimal.