## Unsigned binary (base 2) 1001 1001 0101 1110_{(2)} to a positive integer (no sign) in decimal system (in base 10) = ?

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

2^{15}

1 2^{14}

0 2^{13}

0 2^{12}

1 2^{11}

1 2^{10}

0 2^{9}

0 2^{8}

1 2^{7}

0 2^{6}

1 2^{5}

0 2^{4}

1 2^{3}

1 2^{2}

1 2^{1}

1 2^{0}

0

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

#### 1001 1001 0101 1110_{(2)} =

#### (1 × 2^{15} + 0 × 2^{14} + 0 × 2^{13} + 1 × 2^{12} + 1 × 2^{11} + 0 × 2^{10} + 0 × 2^{9} + 1 × 2^{8} + 0 × 2^{7} + 1 × 2^{6} + 0 × 2^{5} + 1 × 2^{4} + 1 × 2^{3} + 1 × 2^{2} + 1 × 2^{1} + 0 × 2^{0})_{(10)} =

#### (32 768 + 0 + 0 + 4 096 + 2 048 + 0 + 0 + 256 + 0 + 64 + 0 + 16 + 8 + 4 + 2 + 0)_{(10)} =

#### (32 768 + 4 096 + 2 048 + 256 + 64 + 16 + 8 + 4 + 2)_{(10)} =

#### 39 262_{(10)}