Signed Binary Number 0011 0010 Converted and Written as a Decimal System Integer Number (in Base Ten). All the Steps Explained in Detail

The signed binary (in base two) 0011 0010(2) to an integer (with sign) in decimal system (in base ten) = ?

The steps we'll go through to make the conversion:

Construct the unsigned binary number.

Map the unsigned binary number's digits.

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

1. Is this a positive or a negative number?

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.


0011 0010 is the binary representation of a positive integer, on 8 bits.


2. Construct the unsigned binary number.

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


0011 0010 = 011 0010


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

    • 26

      0
    • 25

      1
    • 24

      1
    • 23

      0
    • 22

      0
    • 21

      1
    • 20

      0

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

011 0010(2) =


(0 × 26 + 1 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =


(0 + 32 + 16 + 0 + 0 + 2 + 0)(10) =


(32 + 16 + 2)(10) =


50(10)

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

0011 0010(2) = 50(10)

The number 0011 0010(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0011 0010(2) = 50(10)

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

The signed binary number 0011 0001 (in base two), converted and written as an integer in decimal system (in base ten) = ?

The signed binary number 0011 0011 (in base two), converted and written as an integer in decimal system (in base ten) = ?

Convert signed binary numbers to integers in decimal system (in base ten)

The first bit (the leftmost) is reserved for the sign (1 = negative, 0 = positive) and it doesn't count when calculating the absolute value.

Binary number's length must be: 2, 4, 8, 16, 32, 64 - or else extra bits on 0 are added in front (to the left).

How to convert a signed binary number to an integer in base ten:

1) Construct the unsigned binary number: exclude the first bit (the leftmost); this bit is reserved for the sign, 1 = negative, 0 = positive and does not count when calculating the absolute value (without sign).

2) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

3) Add all the terms up to get the positive integer number in base ten.

4) Adjust the sign of the integer number by the first bit of the initial binary number.

The latest signed binary numbers converted and written as signed integers in decimal system (in base ten)

Convert the signed binary number 0011 0010, write it as a decimal system integer number (written in base ten) Sep 28 00:35 UTC (GMT)
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Convert the signed binary number 1000 0101 0101 0001 1000 1100 0010 1010 1111 1001 0111 1001 0101 0000 1010 1010, write it as a decimal system integer number (written in base ten) Sep 28 00:34 UTC (GMT)
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All the signed binary numbers converted to integers in decimal system (written in base ten)

How to convert signed binary numbers from binary system to decimal (base ten)

To understand how to convert a signed binary number from binary system to decimal (base ten), the easiest way is to do it through an example - convert the binary number, 1001 1110, to base ten:

Available Base Conversions Between Decimal and Binary Systems

Conversions Between Decimal System Numbers (Written in Base Ten) and Binary System Numbers (Base Two and Computer Representation):


1. Integer -> Binary

2. Decimal -> Binary

3. Binary -> Integer

4. Binary -> Decimal