Convert 1 100 110 101 110 101 174 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 100 110 101 110 101 174(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 100 110 101 110 101 174 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;
  • 1 100 110 101 110 101 174 ÷ 2 = 550 055 050 555 050 587 + 0;
  • 550 055 050 555 050 587 ÷ 2 = 275 027 525 277 525 293 + 1;
  • 275 027 525 277 525 293 ÷ 2 = 137 513 762 638 762 646 + 1;
  • 137 513 762 638 762 646 ÷ 2 = 68 756 881 319 381 323 + 0;
  • 68 756 881 319 381 323 ÷ 2 = 34 378 440 659 690 661 + 1;
  • 34 378 440 659 690 661 ÷ 2 = 17 189 220 329 845 330 + 1;
  • 17 189 220 329 845 330 ÷ 2 = 8 594 610 164 922 665 + 0;
  • 8 594 610 164 922 665 ÷ 2 = 4 297 305 082 461 332 + 1;
  • 4 297 305 082 461 332 ÷ 2 = 2 148 652 541 230 666 + 0;
  • 2 148 652 541 230 666 ÷ 2 = 1 074 326 270 615 333 + 0;
  • 1 074 326 270 615 333 ÷ 2 = 537 163 135 307 666 + 1;
  • 537 163 135 307 666 ÷ 2 = 268 581 567 653 833 + 0;
  • 268 581 567 653 833 ÷ 2 = 134 290 783 826 916 + 1;
  • 134 290 783 826 916 ÷ 2 = 67 145 391 913 458 + 0;
  • 67 145 391 913 458 ÷ 2 = 33 572 695 956 729 + 0;
  • 33 572 695 956 729 ÷ 2 = 16 786 347 978 364 + 1;
  • 16 786 347 978 364 ÷ 2 = 8 393 173 989 182 + 0;
  • 8 393 173 989 182 ÷ 2 = 4 196 586 994 591 + 0;
  • 4 196 586 994 591 ÷ 2 = 2 098 293 497 295 + 1;
  • 2 098 293 497 295 ÷ 2 = 1 049 146 748 647 + 1;
  • 1 049 146 748 647 ÷ 2 = 524 573 374 323 + 1;
  • 524 573 374 323 ÷ 2 = 262 286 687 161 + 1;
  • 262 286 687 161 ÷ 2 = 131 143 343 580 + 1;
  • 131 143 343 580 ÷ 2 = 65 571 671 790 + 0;
  • 65 571 671 790 ÷ 2 = 32 785 835 895 + 0;
  • 32 785 835 895 ÷ 2 = 16 392 917 947 + 1;
  • 16 392 917 947 ÷ 2 = 8 196 458 973 + 1;
  • 8 196 458 973 ÷ 2 = 4 098 229 486 + 1;
  • 4 098 229 486 ÷ 2 = 2 049 114 743 + 0;
  • 2 049 114 743 ÷ 2 = 1 024 557 371 + 1;
  • 1 024 557 371 ÷ 2 = 512 278 685 + 1;
  • 512 278 685 ÷ 2 = 256 139 342 + 1;
  • 256 139 342 ÷ 2 = 128 069 671 + 0;
  • 128 069 671 ÷ 2 = 64 034 835 + 1;
  • 64 034 835 ÷ 2 = 32 017 417 + 1;
  • 32 017 417 ÷ 2 = 16 008 708 + 1;
  • 16 008 708 ÷ 2 = 8 004 354 + 0;
  • 8 004 354 ÷ 2 = 4 002 177 + 0;
  • 4 002 177 ÷ 2 = 2 001 088 + 1;
  • 2 001 088 ÷ 2 = 1 000 544 + 0;
  • 1 000 544 ÷ 2 = 500 272 + 0;
  • 500 272 ÷ 2 = 250 136 + 0;
  • 250 136 ÷ 2 = 125 068 + 0;
  • 125 068 ÷ 2 = 62 534 + 0;
  • 62 534 ÷ 2 = 31 267 + 0;
  • 31 267 ÷ 2 = 15 633 + 1;
  • 15 633 ÷ 2 = 7 816 + 1;
  • 7 816 ÷ 2 = 3 908 + 0;
  • 3 908 ÷ 2 = 1 954 + 0;
  • 1 954 ÷ 2 = 977 + 0;
  • 977 ÷ 2 = 488 + 1;
  • 488 ÷ 2 = 244 + 0;
  • 244 ÷ 2 = 122 + 0;
  • 122 ÷ 2 = 61 + 0;
  • 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.

1 100 110 101 110 101 174(10) = 1111 0100 0100 0110 0000 0100 1110 1110 1110 0111 1100 1001 0100 1011 0110(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 60.

  • 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, 60,

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 1 100 110 101 110 101 174(10) converted to signed binary in one's complement representation:

1 100 110 101 110 101 174(10) = 0000 1111 0100 0100 0110 0000 0100 1110 1110 1110 0111 1100 1001 0100 1011 0110

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