#### 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.

### 2. Construct the unsigned binary number.

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

#### 0000 0111 1000 1111 = 000 0111 1000 1111

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

2^{14}

0 2^{13}

0 2^{12}

0 2^{11}

0 2^{10}

1 2^{9}

1 2^{8}

1 2^{7}

1 2^{6}

0 2^{5}

0 2^{4}

0 2^{3}

1 2^{2}

1 2^{1}

1 2^{0}

1

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

#### 000 0111 1000 1111_{(2)} =

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

#### (0 + 0 + 0 + 0 + 1 024 + 512 + 256 + 128 + 0 + 0 + 0 + 8 + 4 + 2 + 1)_{(10)} =

#### (1 024 + 512 + 256 + 128 + 8 + 4 + 2 + 1)_{(10)} =

#### 1 935_{(10)}

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

#### 0000 0111 1000 1111_{(2)} = 1 935_{(10)}

## The number 0000 0111 1000 1111_{(2)} converted from a signed binary (base two) and written as an integer in decimal system (base ten):

0000 0111 1000 1111_{(2)} = 1 935_{(10)}

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