# Base ten decimal system signed integer number 10 111 000 001 converted to signed binary

## How to convert the signed integer in decimal system (in base 10): 10 111 000 001(10) to a signed binary

### 1. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero:

• division = quotient + remainder;
• 10 111 000 001 ÷ 2 = 5 055 500 000 + 1;
• 5 055 500 000 ÷ 2 = 2 527 750 000 + 0;
• 2 527 750 000 ÷ 2 = 1 263 875 000 + 0;
• 1 263 875 000 ÷ 2 = 631 937 500 + 0;
• 631 937 500 ÷ 2 = 315 968 750 + 0;
• 315 968 750 ÷ 2 = 157 984 375 + 0;
• 157 984 375 ÷ 2 = 78 992 187 + 1;
• 78 992 187 ÷ 2 = 39 496 093 + 1;
• 39 496 093 ÷ 2 = 19 748 046 + 1;
• 19 748 046 ÷ 2 = 9 874 023 + 0;
• 9 874 023 ÷ 2 = 4 937 011 + 1;
• 4 937 011 ÷ 2 = 2 468 505 + 1;
• 2 468 505 ÷ 2 = 1 234 252 + 1;
• 1 234 252 ÷ 2 = 617 126 + 0;
• 617 126 ÷ 2 = 308 563 + 0;
• 308 563 ÷ 2 = 154 281 + 1;
• 154 281 ÷ 2 = 77 140 + 1;
• 77 140 ÷ 2 = 38 570 + 0;
• 38 570 ÷ 2 = 19 285 + 0;
• 19 285 ÷ 2 = 9 642 + 1;
• 9 642 ÷ 2 = 4 821 + 0;
• 4 821 ÷ 2 = 2 410 + 1;
• 2 410 ÷ 2 = 1 205 + 0;
• 1 205 ÷ 2 = 602 + 1;
• 602 ÷ 2 = 301 + 0;
• 301 ÷ 2 = 150 + 1;
• 150 ÷ 2 = 75 + 0;
• 75 ÷ 2 = 37 + 1;
• 37 ÷ 2 = 18 + 1;
• 18 ÷ 2 = 9 + 0;
• 9 ÷ 2 = 4 + 1;
• 4 ÷ 2 = 2 + 0;
• 2 ÷ 2 = 1 + 0;
• 1 ÷ 2 = 0 + 1;

## Latest signed integers numbers converted from decimal (base ten) to signed binary

 10,111,000,001 = 0000 0000 0000 0000 0000 0000 0000 0010 0101 1010 1010 1001 1001 1101 1100 0001 May 20 05:11 UTC (GMT) 29 = 0001 1101 May 20 05:08 UTC (GMT) 119 = 0111 0111 May 20 05:08 UTC (GMT) 7,332,565 = 0000 0000 0110 1111 1110 0010 1101 0101 May 20 05:07 UTC (GMT) 11,111,100,000 = 0000 0000 0000 0000 0000 0000 0000 0010 1001 0110 0100 0101 1110 1110 0110 0000 May 20 05:06 UTC (GMT) 483 = 0000 0001 1110 0011 May 20 05:05 UTC (GMT) 146,532 = 0000 0000 0000 0010 0011 1100 0110 0100 May 20 05:01 UTC (GMT) 500,000,000 = 0001 1101 1100 1101 0110 0101 0000 0000 May 20 05:01 UTC (GMT) 193 = 0000 0000 1100 0001 May 20 05:00 UTC (GMT) 972,450 = 0000 0000 0000 1110 1101 0110 1010 0010 May 20 04:55 UTC (GMT) 110,000,110,101,000,000 = 0000 0001 1000 0110 1100 1100 1000 0100 0110 1111 1101 0010 1110 1111 0100 0000 May 20 04:50 UTC (GMT) 30,472 = 0111 0111 0000 1000 May 20 04:49 UTC (GMT) 4,321 = 0001 0000 1110 0001 May 20 04:49 UTC (GMT) All decimal positive integers converted to signed binary

## How to convert signed integers from decimal system to binary code system

### Follow the steps below to convert a signed base ten integer number to signed binary:

• 1. In a signed binary, first bit (the leftmost) is reserved for sign: 0 = positive integer number, 1 = positive integer number. If the number to be converted is negative, start with its positive version.
• 2. Divide repeatedly by 2 the positive integer number keeping track of each remainder. STOP when 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 have a length of 4, 8, 16, 32, 64, ... bits (power of 2) - if needed, fill in extra '0' bits in front of the base 2 number (to the left), up to the right length; this way the first bit (the leftmost one) is always '0', as for a positive representation.
• 5. To get the negative reprezentation of the number, simply switch the first bit (the leftmost one), from '0' to '1'.

### Example: convert the negative number -63 from decimal system (base ten) to signed binary code system:

• 1. Start with the positive version of the number: |-63| = 63;
• 2. Divide repeatedly 63 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
• division = quotient + remainder
• 63 ÷ 2 = 31 + 1
• 31 ÷ 2 = 15 + 1
• 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:
63(10) = 11 1111(2)
• 4. The actual length of base 2 representation number is 6, so the positive binary computer representation length of the signed binary will take in this case 8 bits (the least power of 2 higher than 6) - add extra '0's in front (to the left), up to the required length; this way the first bit (the leftmost one) is to be '0', as for a positive number:
63(10) = 0011 1111(2)
• 5. To get the negative integer number representation simply change the first bit (the leftmost), from '0' to '1':
-63(10) = 1011 1111