## Signed binary 0000 0000 1111 1111 1110 1001 1100 0001_{(2)} to an integer in decimal system (in base 10) = ?

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

#### In a signed binary, 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 1111 1111 1110 1001 1100 0001 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 1111 1111 1110 1001 1100 0001 = 000 0000 1111 1111 1110 1001 1100 0001

### 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}

1 2^{22}

1 2^{21}

1 2^{20}

1 2^{19}

1 2^{18}

1 2^{17}

1 2^{16}

1 2^{15}

1 2^{14}

1 2^{13}

1 2^{12}

0 2^{11}

1 2^{10}

0 2^{9}

0 2^{8}

1 2^{7}

1 2^{6}

1 2^{5}

0 2^{4}

0 2^{3}

0 2^{2}

0 2^{1}

0 2^{0}

1

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

#### 000 0000 1111 1111 1110 1001 1100 0001_{(2)} =

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

#### (0 + 0 + 0 + 0 + 0 + 0 + 0 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 0 + 2 048 + 0 + 0 + 256 + 128 + 64 + 0 + 0 + 0 + 0 + 0 + 1)_{(10)} =

#### (8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 2 048 + 256 + 128 + 64 + 1)_{(10)} =

#### 16 771 521_{(10)}

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

#### 0000 0000 1111 1111 1110 1001 1100 0001_{(2)} = 16 771 521_{(10)}

## Number 0000 0000 1111 1111 1110 1001 1100 0001_{(2)} converted from signed binary to an integer in decimal system (in base 10):

0000 0000 1111 1111 1110 1001 1100 0001_{(2)} = 16 771 521_{(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)

#### 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).