One's Complement: Integer ↗ Binary: 1 011 111 010 100 129 Convert the Integer Number to a Signed Binary in One's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 1 011 111 010 100 129₍₁₀₎ converted and written as a signed binary in one's complement representation (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.

division = quotient + remainder;
1 011 111 010 100 129 ÷ 2 = 505 555 505 050 064 + 1;
505 555 505 050 064 ÷ 2 = 252 777 752 525 032 + 0;
252 777 752 525 032 ÷ 2 = 126 388 876 262 516 + 0;
126 388 876 262 516 ÷ 2 = 63 194 438 131 258 + 0;
63 194 438 131 258 ÷ 2 = 31 597 219 065 629 + 0;
31 597 219 065 629 ÷ 2 = 15 798 609 532 814 + 1;
15 798 609 532 814 ÷ 2 = 7 899 304 766 407 + 0;
7 899 304 766 407 ÷ 2 = 3 949 652 383 203 + 1;
3 949 652 383 203 ÷ 2 = 1 974 826 191 601 + 1;
1 974 826 191 601 ÷ 2 = 987 413 095 800 + 1;
987 413 095 800 ÷ 2 = 493 706 547 900 + 0;
493 706 547 900 ÷ 2 = 246 853 273 950 + 0;
246 853 273 950 ÷ 2 = 123 426 636 975 + 0;
123 426 636 975 ÷ 2 = 61 713 318 487 + 1;
61 713 318 487 ÷ 2 = 30 856 659 243 + 1;
30 856 659 243 ÷ 2 = 15 428 329 621 + 1;
15 428 329 621 ÷ 2 = 7 714 164 810 + 1;
7 714 164 810 ÷ 2 = 3 857 082 405 + 0;
3 857 082 405 ÷ 2 = 1 928 541 202 + 1;
1 928 541 202 ÷ 2 = 964 270 601 + 0;
964 270 601 ÷ 2 = 482 135 300 + 1;
482 135 300 ÷ 2 = 241 067 650 + 0;
241 067 650 ÷ 2 = 120 533 825 + 0;
120 533 825 ÷ 2 = 60 266 912 + 1;
60 266 912 ÷ 2 = 30 133 456 + 0;
30 133 456 ÷ 2 = 15 066 728 + 0;
15 066 728 ÷ 2 = 7 533 364 + 0;
7 533 364 ÷ 2 = 3 766 682 + 0;
3 766 682 ÷ 2 = 1 883 341 + 0;
1 883 341 ÷ 2 = 941 670 + 1;
941 670 ÷ 2 = 470 835 + 0;
470 835 ÷ 2 = 235 417 + 1;
235 417 ÷ 2 = 117 708 + 1;
117 708 ÷ 2 = 58 854 + 0;
58 854 ÷ 2 = 29 427 + 0;
29 427 ÷ 2 = 14 713 + 1;
14 713 ÷ 2 = 7 356 + 1;
7 356 ÷ 2 = 3 678 + 0;
3 678 ÷ 2 = 1 839 + 0;
1 839 ÷ 2 = 919 + 1;
919 ÷ 2 = 459 + 1;
459 ÷ 2 = 229 + 1;
229 ÷ 2 = 114 + 1;
114 ÷ 2 = 57 + 0;
57 ÷ 2 = 28 + 1;
28 ÷ 2 = 14 + 0;
14 ÷ 2 = 7 + 0;
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.

1 011 111 010 100 129₍₁₀₎ = 11 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1010 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.

Number 1 011 111 010 100 129₍₁₀₎, a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

1 011 111 010 100 129₍₁₀₎ = 0000 0000 0000 0011 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1010 0001

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

More operations on signed integers written as signed binary numbers in one's complement representation:

» Signed integer number 1 011 111 010 100 128 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

» Signed integer number 1 011 111 010 100 130 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

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

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One's Complement: Integer ↗ Binary: 1 011 111 010 100 129 Convert the Integer Number to a Signed Binary in One's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 1 011 111 010 100 129₍₁₀₎ converted and written as a signed binary in one's complement representation (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.

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

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

1 011 111 010 100 129₍₁₀₎ = 11 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1010 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.

Number 1 011 111 010 100 129₍₁₀₎, a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

1 011 111 010 100 129₍₁₀₎ = 0000 0000 0000 0011 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1010 0001

More operations on signed integers written as signed binary numbers in one's complement representation:

» Signed integer number 1 011 111 010 100 128 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

» Signed integer number 1 011 111 010 100 130 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

Convert signed integer numbers from the decimal system (base ten) to signed binary in one's complement representation

The latest signed integer numbers converted from decimal system (base ten) and written as signed binary in one's complement representation

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:

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

One's Complement: Integer ↗ Binary: 1 011 111 010 100 129 Convert the Integer Number to a Signed Binary in One's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 1 011 111 010 100 129(10) converted and written as a signed binary in one's complement representation (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.

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

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

1 011 111 010 100 129(10) = 11 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1010 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.

Number 1 011 111 010 100 129(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

1 011 111 010 100 129(10) = 0000 0000 0000 0011 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1010 0001

More operations on signed integers written as signed binary numbers in one's complement representation:

» Signed integer number 1 011 111 010 100 128 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

» Signed integer number 1 011 111 010 100 130 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

The latest signed integer numbers converted from decimal system (base ten) and written as signed binary in one's complement representation

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:

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

Signed integer number 1 011 111 010 100 129₍₁₀₎ converted and written as a signed binary in one's complement representation (base 2) = ?

1 011 111 010 100 129₍₁₀₎ = 11 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1010 0001₍₂₎

2¹ = 2; 2² = 4; 2³ = 8; 2⁴ = 16; 2⁵ = 32; 2⁶ = 64; ...

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

Number 1 011 111 010 100 129₍₁₀₎, a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

1 011 111 010 100 129₍₁₀₎ = 0000 0000 0000 0011 1001 0111 1001 1001 1010 0000 1001 0101 1110 0011 1010 0001