Signed: Binary -> Integer: 1101 0111 1111 0001 0101 0101 0101 0101 Signed Binary Number Converted and Written as a Decimal System Integer (in Base Ten)

The signed binary (in base two) 1101 0111 1111 0001 0101 0101 0101 0101(2) to an integer (with sign) in decimal system (in base ten) = ?

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.

1101 0111 1111 0001 0101 0101 0101 0101 is the binary representation of a negative integer, on 32 bits (4 Bytes).


2. Construct the unsigned binary number.

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

1101 0111 1111 0001 0101 0101 0101 0101 = 101 0111 1111 0001 0101 0101 0101 0101


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

    • 230

      1

    • 229

      0

    • 228

      1

    • 227

      0

    • 226

      1

    • 225

      1

    • 224

      1

    • 223

      1

    • 222

      1

    • 221

      1

    • 220

      1

    • 219

      0

    • 218

      0

    • 217

      0

    • 216

      1

    • 215

      0

    • 214

      1

    • 213

      0

    • 212

      1

    • 211

      0

    • 210

      1

    • 29

      0

    • 28

      1

    • 27

      0

    • 26

      1

    • 25

      0

    • 24

      1

    • 23

      0

    • 22

      1

    • 21

      0

    • 20

      1

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

101 0111 1111 0001 0101 0101 0101 0101(2) =

(1 × 230 + 0 × 229 + 1 × 228 + 0 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 1 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 1 × 216 + 0 × 215 + 1 × 214 + 0 × 213 + 1 × 212 + 0 × 211 + 1 × 210 + 0 × 29 + 1 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =

(1 073 741 824 + 0 + 268 435 456 + 0 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 0 + 0 + 0 + 65 536 + 0 + 16 384 + 0 + 4 096 + 0 + 1 024 + 0 + 256 + 0 + 64 + 0 + 16 + 0 + 4 + 0 + 1)(10) =

(1 073 741 824 + 268 435 456 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 65 536 + 16 384 + 4 096 + 1 024 + 256 + 64 + 16 + 4 + 1)(10) =

1 475 433 813(10)

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

1101 0111 1111 0001 0101 0101 0101 0101(2) = -1 475 433 813(10)

The number 1101 0111 1111 0001 0101 0101 0101 0101(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1101 0111 1111 0001 0101 0101 0101 0101(2) = -1 475 433 813(10)

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

The signed binary number 1101 0111 1111 0001 0101 0101 0101 0100 (in base two), converted and written as an integer in decimal system (in base ten) = ?

The signed binary number 1101 0111 1111 0001 0101 0101 0101 0110 (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 1101 0111 1111 0001 0101 0101 0101 0101, write it as a decimal system integer number (written in base ten) Nov 28 10:41 UTC (GMT)
Convert the signed binary number 0110 0100 0101 1111 1111 1111 1110 1001, write it as a decimal system integer number (written in base ten) Nov 28 10:41 UTC (GMT)
Convert the signed binary number 1100 1100 1101 0010 1011 0100 0111 1101, write it as a decimal system integer number (written in base ten) Nov 28 10:41 UTC (GMT)
Convert the signed binary number 0000 0000 0000 0010 0111 0100 0001 1010, write it as a decimal system integer number (written in base ten) Nov 28 10:40 UTC (GMT)
Convert the signed binary number 0000 0000 0000 0000 0000 0000 0000 0000 1011 0010 1101 0000 0101 1110 0010 1010, write it as a decimal system integer number (written in base ten) Nov 28 10:40 UTC (GMT)
Convert the signed binary number 1100 0100, write it as a decimal system integer number (written in base ten) Nov 28 10:40 UTC (GMT)
Convert the signed binary number 0000 0000 0101 0100 0101 0100 0100 0000 0101 0100 0101 0100 0101 0100 0001 0110, write it as a decimal system integer number (written in base ten) Nov 28 10:39 UTC (GMT)
Convert the signed binary number 1111 1111 1111 1111 1101 1000 1011 1100, write it as a decimal system integer number (written in base ten) Nov 28 10:39 UTC (GMT)
Convert the signed binary number 1010 0101, write it as a decimal system integer number (written in base ten) Nov 28 10:39 UTC (GMT)
Convert the signed binary number 1111 1110 1100 1011 1001 1100 1111 0100, write it as a decimal system integer number (written in base ten) Nov 28 10:38 UTC (GMT)
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:

  • In a signed binary, the first bit (leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value (value without sign). The first bit is 1, so our number is negative.
  • Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number and increasing each corresonding power of 2 by exactly one unit, but ignoring the very first bit (the leftmost, the one representing the sign):
  • powers of 2:   6 5 4 3 2 1 0
    digits: 1 0 0 1 1 1 1 0
  • Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then adding all the terms up, but also taking care of the number sign:

    1001 1110 =

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

    - (0 + 0 + 16 + 8 + 4 + 2 + 0)(10) =

    - (16 + 8 + 4 + 2)(10) =

    -30(10)

  • Binary signed number, 1001 1110 = -30(10), signed negative integer in base 10