0010 1001 Signed Binary Number in Two's Complement Representation, Converted and Written as a Decimal System Integer Number (in Base Ten). Steps Explained in Detail

Signed binary in two's complement representation 0010 1001(2) converted to an integer in decimal system (in base ten) = ?

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

Get the binary representations.

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 two's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.


0010 1001 is the binary representation of a positive integer, on 8 bits.


2. Get the binary representation in one's complement.

* Run this step only if the number is negative *

Note on binary subtraction rules:

11 - 1 = 10; 10 - 1 = 1; 1 - 0 = 1; 1 - 1 = 0.


Subtract 1 from the initial binary number.

* Not the case - the number is positive *


3. 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:

* Not the case - the number is positive *


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

    • 27

      0
    • 26

      0
    • 25

      1
    • 24

      0
    • 23

      1
    • 22

      0
    • 21

      0
    • 20

      1

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

0010 1001(2) =


(0 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20)(10) =


(0 + 0 + 32 + 0 + 8 + 0 + 0 + 1)(10) =


(32 + 8 + 1)(10) =


41(10)

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

0010 1001(2) = 41(10)

The signed binary number in two's complement representation 0010 1001(2) converted and written as an integer in decimal system (base ten):
0010 1001(2) = 41(10)

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

0010 1000 The signed binary in two's complement representation converted and written as an integer number in decimal system (in base ten) = ?

0010 1010 The signed binary in two's complement representation converted and written as an integer number in decimal system (in base ten) = ?

Convert signed binary numbers in two'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 two's complement representation to an integer in base ten:

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

2) Get the signed binary representation in one's complement, subtract 1 from the initial number.

3) 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.

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

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

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

The latest binary numbers written in two\'s complement representation converted to signed integers written in decimal system (in base ten)

Convert the signed binary number written in two's complement representation 0010 1001, write it as a decimal system (base ten) integer Oct 03 15:09 UTC (GMT)
Convert the signed binary number written in two's complement representation 0000 0000 0000 0001 0000 1100 0100 1110 0000 0000 0000 0001 0000 0101 1111 0110, write it as a decimal system (base ten) integer Oct 03 15:08 UTC (GMT)
Convert the signed binary number written in two's complement representation 0011 1010 1001 1100, write it as a decimal system (base ten) integer Oct 03 15:08 UTC (GMT)
Convert the signed binary number written in two's complement representation 1111 1100, write it as a decimal system (base ten) integer Oct 03 15:08 UTC (GMT)
Convert the signed binary number written in two's complement representation 1110 0011 1111 0001, write it as a decimal system (base ten) integer Oct 03 15:07 UTC (GMT)
Convert the signed binary number written in two's complement representation 0000 0010 1000 0000, write it as a decimal system (base ten) integer Oct 03 15:07 UTC (GMT)
Convert the signed binary number written in two's complement representation 1111 1100, write it as a decimal system (base ten) integer Oct 03 15:07 UTC (GMT)
Convert the signed binary number written in two's complement representation 0000 0000 0000 0000 0000 0000 0000 0101 0111 0101 0110 0101 1011 0111 1111 0001, write it as a decimal system (base ten) integer Oct 03 15:07 UTC (GMT)
Convert the signed binary number written in two's complement representation 0100 0001 1011 0000 0000 0000 0010 1000, write it as a decimal system (base ten) integer Oct 03 15:06 UTC (GMT)
Convert the signed binary number written in two's complement representation 1001 0111, write it as a decimal system (base ten) integer Oct 03 15:06 UTC (GMT)
All the signed binary numbers written in two's complement representation converted to decimal system (base ten) integers

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

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