# Convert -2 146 233 054 to a signed binary in two's complement representation, from a signed integer number in base 10 decimal system

## How to convert a signed integer in decimal system (in base 10): -2 146 233 054(10)to a signed binary two's complement representation

### 2. Divide the number repeatedly by 2:

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

• division = quotient + remainder;
• 2 146 233 054 ÷ 2 = 1 073 116 527 + 0;
• 1 073 116 527 ÷ 2 = 536 558 263 + 1;
• 536 558 263 ÷ 2 = 268 279 131 + 1;
• 268 279 131 ÷ 2 = 134 139 565 + 1;
• 134 139 565 ÷ 2 = 67 069 782 + 1;
• 67 069 782 ÷ 2 = 33 534 891 + 0;
• 33 534 891 ÷ 2 = 16 767 445 + 1;
• 16 767 445 ÷ 2 = 8 383 722 + 1;
• 8 383 722 ÷ 2 = 4 191 861 + 0;
• 4 191 861 ÷ 2 = 2 095 930 + 1;
• 2 095 930 ÷ 2 = 1 047 965 + 0;
• 1 047 965 ÷ 2 = 523 982 + 1;
• 523 982 ÷ 2 = 261 991 + 0;
• 261 991 ÷ 2 = 130 995 + 1;
• 130 995 ÷ 2 = 65 497 + 1;
• 65 497 ÷ 2 = 32 748 + 1;
• 32 748 ÷ 2 = 16 374 + 0;
• 16 374 ÷ 2 = 8 187 + 0;
• 8 187 ÷ 2 = 4 093 + 1;
• 4 093 ÷ 2 = 2 046 + 1;
• 2 046 ÷ 2 = 1 023 + 0;
• 1 023 ÷ 2 = 511 + 1;
• 511 ÷ 2 = 255 + 1;
• 255 ÷ 2 = 127 + 1;
• 127 ÷ 2 = 63 + 1;
• 63 ÷ 2 = 31 + 1;
• 31 ÷ 2 = 15 + 1;
• 15 ÷ 2 = 7 + 1;
• 7 ÷ 2 = 3 + 1;
• 3 ÷ 2 = 1 + 1;
• 1 ÷ 2 = 0 + 1;

## Latest signed integers converted from decimal system to binary two's complement representation

 -2,146,233,054 to signed binary two's complement = ? Nov 25 20:30 UTC (GMT) 2,435 to signed binary two's complement = ? Nov 25 20:30 UTC (GMT) 18,970 to signed binary two's complement = ? Nov 25 20:30 UTC (GMT) 38,537 to signed binary two's complement = ? Nov 25 20:30 UTC (GMT) -1,126,269,741 to signed binary two's complement = ? Nov 25 20:29 UTC (GMT) 110,100 to signed binary two's complement = ? Nov 25 20:29 UTC (GMT) 11,001,113 to signed binary two's complement = ? Nov 25 20:29 UTC (GMT) 497 to signed binary two's complement = ? Nov 25 20:28 UTC (GMT) -934 to signed binary two's complement = ? Nov 25 20:28 UTC (GMT) 342 to signed binary two's complement = ? Nov 25 20:28 UTC (GMT) -81 to signed binary two's complement = ? Nov 25 20:28 UTC (GMT) -225 to signed binary two's complement = ? Nov 25 20:28 UTC (GMT) -13,847 to signed binary two's complement = ? Nov 25 20:28 UTC (GMT) All decimal integer numbers converted to signed binary two's complement representation

## How to convert signed integers from decimal system to signed binary in two's complement representation

### Follow the steps below to convert a signed base 10 integer number to signed binary in two'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, keeping track of each remainder, until we get a quotient that is 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, add extra bits on 0 in front (to the left) of the base 2 number above, up to the required length, so that the first bit (the leftmost) will 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 1s and all 1 bits with 0s (reversing the digits).
• 6. To get the negative integer number, in signed binary two's complement representation, add 1 to the number above.

### Example: convert the negative number -60 from the decimal system (base ten) to signed binary in two's complement:

• 1. Start with the positive version of the number: |-60| = 60
• 2. Divide repeatedly 60 by 2, keeping track of each remainder:
• division = quotient + remainder
• 60 ÷ 2 = 30 + 0
• 30 ÷ 2 = 15 + 0
• 15 ÷ 2 = 7 + 1
• 7 ÷ 2 = 3 + 1
• 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:
60(10) = 11 1100(2)
• 4. Bit length of base 2 representation number is 6, so the positive binary computer representation of a signed binary will take in this particular case 8 bits (the least power of 2 larger than 6) - add extra 0 digits in front of the base 2 number, up to the required length:
60(10) = 0011 1100(2)
• 5. To get the negative integer number representation in signed binary one's complement, replace all the 0 bits with 1s and all 1 bits with 0s (reversing the digits):
!(0011 1100) = 1100 0011
• 6. To get the negative integer number, signed binary in two's complement representation, add 1 to the number above:
-60(10) = 1100 0011 + 1 = 1100 0100