1011 1001 1010 0110 Signed Binary Number in One's Complement Representation, Converted and Written as a Decimal System Integer Number (in Base Ten). Steps Explained in Detail

Signed binary in one's complement representation 1011 1001 1010 0110(2) converted to an integer in decimal system (in base ten) = ?

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

Get the binary representation of the positive (unsigned) 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 in one's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.


1011 1001 1010 0110 is the binary representation of a negative integer, on 16 bits (2 Bytes).


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:

!(1011 1001 1010 0110) = 0100 0110 0101 1001


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

    • 215

      0
    • 214

      1
    • 213

      0
    • 212

      0
    • 211

      0
    • 210

      1
    • 29

      1
    • 28

      0
    • 27

      0
    • 26

      1
    • 25

      0
    • 24

      1
    • 23

      1
    • 22

      0
    • 21

      0
    • 20

      1

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

0100 0110 0101 1001(2) =


(0 × 215 + 1 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 1 × 210 + 1 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20)(10) =


(0 + 16 384 + 0 + 0 + 0 + 1 024 + 512 + 0 + 0 + 64 + 0 + 16 + 8 + 0 + 0 + 1)(10) =


(16 384 + 1 024 + 512 + 64 + 16 + 8 + 1)(10) =


18 009(10)

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

1011 1001 1010 0110(2) = -18 009(10)

The signed binary number in one's complement representation 1011 1001 1010 0110(2) converted and written as an integer in decimal system (base ten):
1011 1001 1010 0110(2) = -18 009(10)

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

The signed binary in one's complement representation 1011 1001 1010 0101 converted and written as an integer number in decimal system (in base ten) = ?

The signed binary in one's complement representation 1011 1001 1010 0111 converted and written as an integer number in decimal system (in base ten) = ?

Convert signed binary numbers in one's complement representation to decimal system (base ten) integers

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 in one's complement representation to an integer in base ten:

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

2) Construct the unsigned binary number: flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s.

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

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

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

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How to convert signed binary numbers in one's complement representation from binary system to decimal

To understand how to convert a signed binary number in one's complement representation from binary system to decimal (base ten), the easiest way is to do it through an example - convert binary, 1001 1101, 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