# Signed Binary Number 0010 1110 1001 1101 Converted and Written as a Decimal System Integer Number (in Base Ten). All the Steps Explained in Detail

## The signed binary (in base two) 0010 1110 1001 1101_{(2)} to an integer (with sign) in decimal system (in base ten) = ?

### The steps we'll go through to make the conversion:

#### Construct the unsigned binary number.

#### Map the unsigned binary number's digits.

#### Multiply each bit by its corresponding power of 2 and add all the terms up.

### 1. Is this a positive or a negative number?

#### In a signed binary, the first bit (the leftmost) is reserved for the sign,

#### 1 = negative, 0 = positive. This bit does not count when calculating the absolute value.

#### 0010 1110 1001 1101 is the binary representation of a positive integer, on 16 bits (2 Bytes).

### 2. Construct the unsigned binary number.

#### Exclude the first bit (the leftmost), that is reserved for the sign:

#### 0010 1110 1001 1101 = 010 1110 1001 1101

### 3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:

2^{14}

0 2^{13}

1 2^{12}

0 2^{11}

1 2^{10}

1 2^{9}

1 2^{8}

0 2^{7}

1 2^{6}

0 2^{5}

0 2^{4}

1 2^{3}

1 2^{2}

1 2^{1}

0 2^{0}

1

### 4. Multiply each bit by its corresponding power of 2 and add all the terms up.

#### 010 1110 1001 1101_{(2)} =

#### (0 × 2^{14} + 1 × 2^{13} + 0 × 2^{12} + 1 × 2^{11} + 1 × 2^{10} + 1 × 2^{9} + 0 × 2^{8} + 1 × 2^{7} + 0 × 2^{6} + 0 × 2^{5} + 1 × 2^{4} + 1 × 2^{3} + 1 × 2^{2} + 0 × 2^{1} + 1 × 2^{0})_{(10)} =

#### (0 + 8 192 + 0 + 2 048 + 1 024 + 512 + 0 + 128 + 0 + 0 + 16 + 8 + 4 + 0 + 1)_{(10)} =

#### (8 192 + 2 048 + 1 024 + 512 + 128 + 16 + 8 + 4 + 1)_{(10)} =

#### 11 933_{(10)}

### 5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:

#### 0010 1110 1001 1101_{(2)} = 11 933_{(10)}

## The number 0010 1110 1001 1101_{(2)} converted from a signed binary (base two) and written as an integer in decimal system (base ten):

0010 1110 1001 1101_{(2)} = 11 933_{(10)}

#### Spaces were used to group digits: for binary, by 4, for decimal, by 3.

## Convert signed binary numbers to integers in decimal system (in base ten)

#### The first bit (the leftmost) is reserved for the sign (1 = negative, 0 = positive) and it doesn't count when calculating the absolute value.

#### Binary number's length must be: 2, 4, 8, 16, 32, 64 - or else extra bits on 0 are added in front (to the left).

### How to convert a signed binary number to an integer in base ten:

#### 1) Construct the unsigned binary number: exclude the first bit (the leftmost); this bit is reserved for the sign, 1 = negative, 0 = positive and does not count when calculating the absolute value (without sign).

#### 2) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

#### 3) Add all the terms up to get the positive integer number in base ten.

#### 4) Adjust the sign of the integer number by the first bit of the initial binary number.

## The latest signed binary numbers converted and written as signed integers in decimal system (in base ten)

** Convert the signed binary number 0010 1110 1001 1101, write it as a decimal system integer number (written in base ten) ** | * Sep 28 01:14 UTC (GMT)* |

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** All the signed binary numbers converted to integers in decimal system (written in base ten) ** |

## How to convert signed binary numbers from binary system to decimal (base ten)

### To understand how to convert a signed binary number from binary system to decimal (base ten), the easiest way is to do it through an example - convert the binary number, 1001 1110, to base ten:

## Available Base Conversions Between Decimal and Binary Systems

### Conversions Between Decimal System Numbers (Written in Base Ten) and Binary System Numbers (Base Two and Computer Representation):

### 1. Integer -> Binary

### 2. Decimal -> Binary

### 3. Binary -> Integer

### 4. Binary -> Decimal