# Signed: Binary -> Integer: 0010 0101 1010 0010 1111 1001 1001 1000 Signed Binary Number Converted and Written as a Decimal System Integer (in Base Ten)

## The signed binary (in base two) 0010 0101 1010 0010 1111 1001 1001 1000_{(2)} to an integer (with sign) in decimal system (in base ten) = ?

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

#### 0010 0101 1010 0010 1111 1001 1001 1000 is the binary representation of a positive integer, on 32 bits (4 Bytes).

#### 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:

#### 0010 0101 1010 0010 1111 1001 1001 1000 = 010 0101 1010 0010 1111 1001 1001 1000

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

2^{30}

0 2^{29}

1 2^{28}

0 2^{27}

0 2^{26}

1 2^{25}

0 2^{24}

1 2^{23}

1 2^{22}

0 2^{21}

1 2^{20}

0 2^{19}

0 2^{18}

0 2^{17}

1 2^{16}

0 2^{15}

1 2^{14}

1 2^{13}

1 2^{12}

1 2^{11}

1 2^{10}

0 2^{9}

0 2^{8}

1 2^{7}

1 2^{6}

0 2^{5}

0 2^{4}

1 2^{3}

1 2^{2}

0 2^{1}

0 2^{0}

0

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

#### 010 0101 1010 0010 1111 1001 1001 1000_{(2)} =

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

#### (0 + 536 870 912 + 0 + 0 + 67 108 864 + 0 + 16 777 216 + 8 388 608 + 0 + 2 097 152 + 0 + 0 + 0 + 131 072 + 0 + 32 768 + 16 384 + 8 192 + 4 096 + 2 048 + 0 + 0 + 256 + 128 + 0 + 0 + 16 + 8 + 0 + 0 + 0)_{(10)} =

#### (536 870 912 + 67 108 864 + 16 777 216 + 8 388 608 + 2 097 152 + 131 072 + 32 768 + 16 384 + 8 192 + 4 096 + 2 048 + 256 + 128 + 16 + 8)_{(10)} =

#### 631 437 720_{(10)}

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

#### 0010 0101 1010 0010 1111 1001 1001 1000_{(2)} = 631 437 720_{(10)}

## The number 0010 0101 1010 0010 1111 1001 1001 1000_{(2)} converted from a signed binary (base two) and written as an integer in decimal system (base ten):

0010 0101 1010 0010 1111 1001 1001 1000_{(2)} = 631 437 720_{(10)}

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