One's Complement: Integer ↗ Binary: 1 011 000 010 010 090 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 1 011 000 010 010 090₍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;
1 011 000 010 010 090 ÷ 2 = 505 500 005 005 045 + 0;
505 500 005 005 045 ÷ 2 = 252 750 002 502 522 + 1;
252 750 002 502 522 ÷ 2 = 126 375 001 251 261 + 0;
126 375 001 251 261 ÷ 2 = 63 187 500 625 630 + 1;
63 187 500 625 630 ÷ 2 = 31 593 750 312 815 + 0;
31 593 750 312 815 ÷ 2 = 15 796 875 156 407 + 1;
15 796 875 156 407 ÷ 2 = 7 898 437 578 203 + 1;
7 898 437 578 203 ÷ 2 = 3 949 218 789 101 + 1;
3 949 218 789 101 ÷ 2 = 1 974 609 394 550 + 1;
1 974 609 394 550 ÷ 2 = 987 304 697 275 + 0;
987 304 697 275 ÷ 2 = 493 652 348 637 + 1;
493 652 348 637 ÷ 2 = 246 826 174 318 + 1;
246 826 174 318 ÷ 2 = 123 413 087 159 + 0;
123 413 087 159 ÷ 2 = 61 706 543 579 + 1;
61 706 543 579 ÷ 2 = 30 853 271 789 + 1;
30 853 271 789 ÷ 2 = 15 426 635 894 + 1;
15 426 635 894 ÷ 2 = 7 713 317 947 + 0;
7 713 317 947 ÷ 2 = 3 856 658 973 + 1;
3 856 658 973 ÷ 2 = 1 928 329 486 + 1;
1 928 329 486 ÷ 2 = 964 164 743 + 0;
964 164 743 ÷ 2 = 482 082 371 + 1;
482 082 371 ÷ 2 = 241 041 185 + 1;
241 041 185 ÷ 2 = 120 520 592 + 1;
120 520 592 ÷ 2 = 60 260 296 + 0;
60 260 296 ÷ 2 = 30 130 148 + 0;
30 130 148 ÷ 2 = 15 065 074 + 0;
15 065 074 ÷ 2 = 7 532 537 + 0;
7 532 537 ÷ 2 = 3 766 268 + 1;
3 766 268 ÷ 2 = 1 883 134 + 0;
1 883 134 ÷ 2 = 941 567 + 0;
941 567 ÷ 2 = 470 783 + 1;
470 783 ÷ 2 = 235 391 + 1;
235 391 ÷ 2 = 117 695 + 1;
117 695 ÷ 2 = 58 847 + 1;
58 847 ÷ 2 = 29 423 + 1;
29 423 ÷ 2 = 14 711 + 1;
14 711 ÷ 2 = 7 355 + 1;
7 355 ÷ 2 = 3 677 + 1;
3 677 ÷ 2 = 1 838 + 1;
1 838 ÷ 2 = 919 + 0;
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.

1 011 000 010 010 090₍₁₀₎ = 11 1001 0111 0111 1111 1100 1000 0111 0110 1110 1101 1110 1010₍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 1 011 000 010 010 090₍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:

1 011 000 010 010 090₍₁₀₎ = 0000 0000 0000 0011 1001 0111 0111 1111 1100 1000 0111 0110 1110 1101 1110 1010

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 1 011 000 010 010 089 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 1 011 000 010 010 091 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: 1 011 000 010 010 090 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 1 011 000 010 010 090₍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.

1 011 000 010 010 090₍₁₀₎ = 11 1001 0111 0111 1111 1100 1000 0111 0110 1110 1101 1110 1010₍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 1 011 000 010 010 090₍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:

1 011 000 010 010 090₍₁₀₎ = 0000 0000 0000 0011 1001 0111 0111 1111 1100 1000 0111 0110 1110 1101 1110 1010

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

» Signed integer number 1 011 000 010 010 089 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 1 011 000 010 010 091 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: 1 011 000 010 010 090 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 1 011 000 010 010 090(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.

1 011 000 010 010 090(10) = 11 1001 0111 0111 1111 1100 1000 0111 0110 1110 1101 1110 1010(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 1 011 000 010 010 090(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:

1 011 000 010 010 090(10) = 0000 0000 0000 0011 1001 0111 0111 1111 1100 1000 0111 0110 1110 1101 1110 1010

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

» Signed integer number 1 011 000 010 010 089 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 1 011 000 010 010 091 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 1 011 000 010 010 090₍₁₀₎ converted and written as a signed binary in one's complement representation (base 2) = ?

1 011 000 010 010 090₍₁₀₎ = 11 1001 0111 0111 1111 1100 1000 0111 0110 1110 1101 1110 1010₍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 1 011 000 010 010 090₍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:

1 011 000 010 010 090₍₁₀₎ = 0000 0000 0000 0011 1001 0111 0111 1111 1100 1000 0111 0110 1110 1101 1110 1010