# One's Complement: Binary -> Integer: 0000 0000 0000 1011 1010 0111 1010 0001 Signed Binary Number in One's Complement Representation, Converted and Written as a Decimal System Integer (in Base Ten)

## Signed binary in one's complement representation 0000 0000 0000 1011 1010 0111 1010 0001_{(2)} converted to an integer in decimal system (in base ten) = ?

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

#### 0000 0000 0000 1011 1010 0111 1010 0001 is the binary representation of a positive integer, on 32 bits (4 Bytes).

#### In a signed binary in one's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.

### 2. Get the binary representation of the positive (unsigned) number.

#### * Run this step only if the number is negative *

#### Flip all the bits of the signed binary in one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:

#### * Not the case - the number is positive *

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

2^{31}

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}

1 2^{18}

0 2^{17}

1 2^{16}

1 2^{15}

1 2^{14}

0 2^{13}

1 2^{12}

0 2^{11}

0 2^{10}

1 2^{9}

1 2^{8}

1 2^{7}

1 2^{6}

0 2^{5}

1 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.

#### 0000 0000 0000 1011 1010 0111 1010 0001_{(2)} =

#### (0 × 2^{31} + 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} + 1 × 2^{19} + 0 × 2^{18} + 1 × 2^{17} + 1 × 2^{16} + 1 × 2^{15} + 0 × 2^{14} + 1 × 2^{13} + 0 × 2^{12} + 0 × 2^{11} + 1 × 2^{10} + 1 × 2^{9} + 1 × 2^{8} + 1 × 2^{7} + 0 × 2^{6} + 1 × 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 + 0 + 0 + 0 + 0 + 0 + 524 288 + 0 + 131 072 + 65 536 + 32 768 + 0 + 8 192 + 0 + 0 + 1 024 + 512 + 256 + 128 + 0 + 32 + 0 + 0 + 0 + 0 + 1)_{(10)} =

#### (524 288 + 131 072 + 65 536 + 32 768 + 8 192 + 1 024 + 512 + 256 + 128 + 32 + 1)_{(10)} =

#### 763 809_{(10)}

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

#### 0000 0000 0000 1011 1010 0111 1010 0001_{(2)} = 763 809_{(10)}

## The signed binary number in one's complement representation 0000 0000 0000 1011 1010 0111 1010 0001_{(2)} converted and written as an integer in decimal system (base ten):

0000 0000 0000 1011 1010 0111 1010 0001_{(2)} = 763 809_{(10)}

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