# Signed binary number 0000 0000 0000 0000 0010 0001 1011 0011 converted to an integer in base ten

## Signed binary 0000 0000 0000 0000 0010 0001 1011 0011_{(2)} to an integer in decimal system (in base 10) = ?

### 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.

#### 0000 0000 0000 0000 0010 0001 1011 0011 is the binary representation of a positive integer, on 32 bits (4 Bytes).

### 2. Construct the unsigned binary number.

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

#### 0000 0000 0000 0000 0010 0001 1011 0011 = 000 0000 0000 0000 0010 0001 1011 0011

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

2^{30}

0 2^{29}

0 2^{28}

0 2^{27}

0 2^{26}

0 2^{25}

0 2^{24}

0 2^{23}

0 2^{22}

0 2^{21}

0 2^{20}

0 2^{19}

0 2^{18}

0 2^{17}

0 2^{16}

0 2^{15}

0 2^{14}

0 2^{13}

1 2^{12}

0 2^{11}

0 2^{10}

0 2^{9}

0 2^{8}

1 2^{7}

1 2^{6}

0 2^{5}

1 2^{4}

1 2^{3}

0 2^{2}

0 2^{1}

1 2^{0}

1

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

#### 000 0000 0000 0000 0010 0001 1011 0011_{(2)} =

#### (0 × 2^{30} + 0 × 2^{29} + 0 × 2^{28} + 0 × 2^{27} + 0 × 2^{26} + 0 × 2^{25} + 0 × 2^{24} + 0 × 2^{23} + 0 × 2^{22} + 0 × 2^{21} + 0 × 2^{20} + 0 × 2^{19} + 0 × 2^{18} + 0 × 2^{17} + 0 × 2^{16} + 0 × 2^{15} + 0 × 2^{14} + 1 × 2^{13} + 0 × 2^{12} + 0 × 2^{11} + 0 × 2^{10} + 0 × 2^{9} + 1 × 2^{8} + 1 × 2^{7} + 0 × 2^{6} + 1 × 2^{5} + 1 × 2^{4} + 0 × 2^{3} + 0 × 2^{2} + 1 × 2^{1} + 1 × 2^{0})_{(10)} =

#### (0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 8 192 + 0 + 0 + 0 + 0 + 256 + 128 + 0 + 32 + 16 + 0 + 0 + 2 + 1)_{(10)} =

#### (8 192 + 256 + 128 + 32 + 16 + 2 + 1)_{(10)} =

#### 8 627_{(10)}

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

#### 0000 0000 0000 0000 0010 0001 1011 0011_{(2)} = 8 627_{(10)}

## Number 0000 0000 0000 0000 0010 0001 1011 0011_{(2)} converted from signed binary to an integer in decimal system (in base 10):

0000 0000 0000 0000 0010 0001 1011 0011_{(2)} = 8 627_{(10)}

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

### More operations of this kind:

## Convert signed binary numbers to integers in decimal system (base 10)

#### The first bit (the leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value.

#### Entered binary number length must be: 2, 4, 8, 16, 32, or 64 - otherwise extra bits on 0 will be 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.

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

** 0000 0000 0000 0000 0010 0001 1011 0011 converted from: signed binary, to signed integer = 8,627 ** | * May 29 15:15 UTC (GMT)* |

** 0000 0000 0101 0101 0101 0100 0100 0011 0100 0011 0100 0101 0100 0011 0100 0000 converted from: signed binary, to signed integer = 24,018,020,888,560,448 ** | * May 29 15:14 UTC (GMT)* |

** 0100 0010 1010 1001 1111 1111 1110 1000 converted from: signed binary, to signed integer = 1,118,437,352 ** | * May 29 15:14 UTC (GMT)* |

** 0000 0000 0000 0010 1101 0100 0001 0010 converted from: signed binary, to signed integer = 185,362 ** | * May 29 15:14 UTC (GMT)* |

** 0001 0011 1100 1101 converted from: signed binary, to signed integer = 5,069 ** | * May 29 15:13 UTC (GMT)* |

** 0000 0000 0000 0000 1111 1110 1101 0011 converted from: signed binary, to signed integer = 65,235 ** | * May 29 15:12 UTC (GMT)* |

** 0100 0000 1010 0000 0000 0000 0001 0110 converted from: signed binary, to signed integer = 1,084,227,606 ** | * May 29 15:12 UTC (GMT)* |

** 0000 0000 1000 1100 1100 0010 1100 0100 1101 0010 1100 0010 1101 1100 0010 1101 converted from: signed binary, to signed integer = 39,620,647,344,856,109 ** | * May 29 15:12 UTC (GMT)* |

** 0010 0100 0010 0100 0000 0001 0000 0100 0000 0001 0010 0100 1010 1010 1000 1010 converted from: signed binary, to signed integer = 2,604,207,601,237,666,442 ** | * May 29 15:11 UTC (GMT)* |

** 1100 1010 converted from: signed binary, to signed integer = -74 ** | * May 29 15:11 UTC (GMT)* |

** 1001 1110 1101 0001 converted from: signed binary, to signed integer = -7,889 ** | * May 29 15:11 UTC (GMT)* |

** 0000 0000 0000 0000 0000 0000 0000 0000 1111 1111 1111 1111 1111 1111 1111 1001 converted from: signed binary, to signed integer = 4,294,967,289 ** | * May 29 15:11 UTC (GMT)* |

** 1010 1001 converted from: signed binary, to signed integer = -41 ** | * May 29 15:11 UTC (GMT)* |

** All the converted signed binary numbers to integers 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: