Convert 34 056 995 640 531 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 34 056 995 640 531(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
34 056 995 640 531 to a signed binary in one's (1's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 34 056 995 640 531 ÷ 2 = 17 028 497 820 265 + 1;
  • 17 028 497 820 265 ÷ 2 = 8 514 248 910 132 + 1;
  • 8 514 248 910 132 ÷ 2 = 4 257 124 455 066 + 0;
  • 4 257 124 455 066 ÷ 2 = 2 128 562 227 533 + 0;
  • 2 128 562 227 533 ÷ 2 = 1 064 281 113 766 + 1;
  • 1 064 281 113 766 ÷ 2 = 532 140 556 883 + 0;
  • 532 140 556 883 ÷ 2 = 266 070 278 441 + 1;
  • 266 070 278 441 ÷ 2 = 133 035 139 220 + 1;
  • 133 035 139 220 ÷ 2 = 66 517 569 610 + 0;
  • 66 517 569 610 ÷ 2 = 33 258 784 805 + 0;
  • 33 258 784 805 ÷ 2 = 16 629 392 402 + 1;
  • 16 629 392 402 ÷ 2 = 8 314 696 201 + 0;
  • 8 314 696 201 ÷ 2 = 4 157 348 100 + 1;
  • 4 157 348 100 ÷ 2 = 2 078 674 050 + 0;
  • 2 078 674 050 ÷ 2 = 1 039 337 025 + 0;
  • 1 039 337 025 ÷ 2 = 519 668 512 + 1;
  • 519 668 512 ÷ 2 = 259 834 256 + 0;
  • 259 834 256 ÷ 2 = 129 917 128 + 0;
  • 129 917 128 ÷ 2 = 64 958 564 + 0;
  • 64 958 564 ÷ 2 = 32 479 282 + 0;
  • 32 479 282 ÷ 2 = 16 239 641 + 0;
  • 16 239 641 ÷ 2 = 8 119 820 + 1;
  • 8 119 820 ÷ 2 = 4 059 910 + 0;
  • 4 059 910 ÷ 2 = 2 029 955 + 0;
  • 2 029 955 ÷ 2 = 1 014 977 + 1;
  • 1 014 977 ÷ 2 = 507 488 + 1;
  • 507 488 ÷ 2 = 253 744 + 0;
  • 253 744 ÷ 2 = 126 872 + 0;
  • 126 872 ÷ 2 = 63 436 + 0;
  • 63 436 ÷ 2 = 31 718 + 0;
  • 31 718 ÷ 2 = 15 859 + 0;
  • 15 859 ÷ 2 = 7 929 + 1;
  • 7 929 ÷ 2 = 3 964 + 1;
  • 3 964 ÷ 2 = 1 982 + 0;
  • 1 982 ÷ 2 = 991 + 0;
  • 991 ÷ 2 = 495 + 1;
  • 495 ÷ 2 = 247 + 1;
  • 247 ÷ 2 = 123 + 1;
  • 123 ÷ 2 = 61 + 1;
  • 61 ÷ 2 = 30 + 1;
  • 30 ÷ 2 = 15 + 0;
  • 15 ÷ 2 = 7 + 1;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

34 056 995 640 531(10) = 1 1110 1111 1001 1000 0011 0010 0000 1001 0100 1101 0011(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 45.

  • A signed binary's bit length must be equal to a power of 2, as of:
  • 21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
  • The first bit (the leftmost) indicates the sign:
  • 0 = positive integer number, 1 = negative integer number

The least number that is:

1) a power of 2

2) and is larger than the actual length, 45,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. Get the positive binary computer representation on 64 bits (8 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.


Decimal Number 34 056 995 640 531(10) converted to signed binary in one's complement representation:

34 056 995 640 531(10) = 0000 0000 0000 0000 0001 1110 1111 1001 1000 0011 0010 0000 1001 0100 1101 0011

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

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

Follow the steps below to convert a signed base 10 integer number to signed binary in one's complement representation:

  • 1. If the number to be converted is negative, start with the positive version of the number.
  • 2. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to ZERO.
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
  • 4. Binary numbers represented in computer language must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always be '0', correctly representing a positive number.
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's.

Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 49 ÷ 2 = 24 + 1
    • 24 ÷ 2 = 12 + 0
    • 12 ÷ 2 = 6 + 0
    • 6 ÷ 2 = 3 + 0
    • 3 ÷ 2 = 1 + 1
    • 1 ÷ 2 = 0 + 1
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:
    49(10) = 11 0001(2)
  • 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:
    -49(10) = 1100 1110
  • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110