Convert 1 100 101 110 010 145 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 100 101 110 010 145(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 100 101 110 010 145 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;
  • 1 100 101 110 010 145 ÷ 2 = 550 050 555 005 072 + 1;
  • 550 050 555 005 072 ÷ 2 = 275 025 277 502 536 + 0;
  • 275 025 277 502 536 ÷ 2 = 137 512 638 751 268 + 0;
  • 137 512 638 751 268 ÷ 2 = 68 756 319 375 634 + 0;
  • 68 756 319 375 634 ÷ 2 = 34 378 159 687 817 + 0;
  • 34 378 159 687 817 ÷ 2 = 17 189 079 843 908 + 1;
  • 17 189 079 843 908 ÷ 2 = 8 594 539 921 954 + 0;
  • 8 594 539 921 954 ÷ 2 = 4 297 269 960 977 + 0;
  • 4 297 269 960 977 ÷ 2 = 2 148 634 980 488 + 1;
  • 2 148 634 980 488 ÷ 2 = 1 074 317 490 244 + 0;
  • 1 074 317 490 244 ÷ 2 = 537 158 745 122 + 0;
  • 537 158 745 122 ÷ 2 = 268 579 372 561 + 0;
  • 268 579 372 561 ÷ 2 = 134 289 686 280 + 1;
  • 134 289 686 280 ÷ 2 = 67 144 843 140 + 0;
  • 67 144 843 140 ÷ 2 = 33 572 421 570 + 0;
  • 33 572 421 570 ÷ 2 = 16 786 210 785 + 0;
  • 16 786 210 785 ÷ 2 = 8 393 105 392 + 1;
  • 8 393 105 392 ÷ 2 = 4 196 552 696 + 0;
  • 4 196 552 696 ÷ 2 = 2 098 276 348 + 0;
  • 2 098 276 348 ÷ 2 = 1 049 138 174 + 0;
  • 1 049 138 174 ÷ 2 = 524 569 087 + 0;
  • 524 569 087 ÷ 2 = 262 284 543 + 1;
  • 262 284 543 ÷ 2 = 131 142 271 + 1;
  • 131 142 271 ÷ 2 = 65 571 135 + 1;
  • 65 571 135 ÷ 2 = 32 785 567 + 1;
  • 32 785 567 ÷ 2 = 16 392 783 + 1;
  • 16 392 783 ÷ 2 = 8 196 391 + 1;
  • 8 196 391 ÷ 2 = 4 098 195 + 1;
  • 4 098 195 ÷ 2 = 2 049 097 + 1;
  • 2 049 097 ÷ 2 = 1 024 548 + 1;
  • 1 024 548 ÷ 2 = 512 274 + 0;
  • 512 274 ÷ 2 = 256 137 + 0;
  • 256 137 ÷ 2 = 128 068 + 1;
  • 128 068 ÷ 2 = 64 034 + 0;
  • 64 034 ÷ 2 = 32 017 + 0;
  • 32 017 ÷ 2 = 16 008 + 1;
  • 16 008 ÷ 2 = 8 004 + 0;
  • 8 004 ÷ 2 = 4 002 + 0;
  • 4 002 ÷ 2 = 2 001 + 0;
  • 2 001 ÷ 2 = 1 000 + 1;
  • 1 000 ÷ 2 = 500 + 0;
  • 500 ÷ 2 = 250 + 0;
  • 250 ÷ 2 = 125 + 0;
  • 125 ÷ 2 = 62 + 1;
  • 62 ÷ 2 = 31 + 0;
  • 31 ÷ 2 = 15 + 1;
  • 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.

1 100 101 110 010 145(10) = 11 1110 1000 1000 1001 0011 1111 1110 0001 0001 0001 0010 0001(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 50.

  • 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, 50,

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 1 100 101 110 010 145(10) converted to signed binary in one's complement representation:

1 100 101 110 010 145(10) = 0000 0000 0000 0011 1110 1000 1000 1001 0011 1111 1110 0001 0001 0001 0010 0001

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