# Base ten decimal system signed integer number 101 111 001 100 converted to signed binary

## How to convert the signed integer in decimal system (in base 10): 101 111 001 100(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;
• 101 111 001 100 ÷ 2 = 50 555 500 550 + 0;
• 50 555 500 550 ÷ 2 = 25 277 750 275 + 0;
• 25 277 750 275 ÷ 2 = 12 638 875 137 + 1;
• 12 638 875 137 ÷ 2 = 6 319 437 568 + 1;
• 6 319 437 568 ÷ 2 = 3 159 718 784 + 0;
• 3 159 718 784 ÷ 2 = 1 579 859 392 + 0;
• 1 579 859 392 ÷ 2 = 789 929 696 + 0;
• 789 929 696 ÷ 2 = 394 964 848 + 0;
• 394 964 848 ÷ 2 = 197 482 424 + 0;
• 197 482 424 ÷ 2 = 98 741 212 + 0;
• 98 741 212 ÷ 2 = 49 370 606 + 0;
• 49 370 606 ÷ 2 = 24 685 303 + 0;
• 24 685 303 ÷ 2 = 12 342 651 + 1;
• 12 342 651 ÷ 2 = 6 171 325 + 1;
• 6 171 325 ÷ 2 = 3 085 662 + 1;
• 3 085 662 ÷ 2 = 1 542 831 + 0;
• 1 542 831 ÷ 2 = 771 415 + 1;
• 771 415 ÷ 2 = 385 707 + 1;
• 385 707 ÷ 2 = 192 853 + 1;
• 192 853 ÷ 2 = 96 426 + 1;
• 96 426 ÷ 2 = 48 213 + 0;
• 48 213 ÷ 2 = 24 106 + 1;
• 24 106 ÷ 2 = 12 053 + 0;
• 12 053 ÷ 2 = 6 026 + 1;
• 6 026 ÷ 2 = 3 013 + 0;
• 3 013 ÷ 2 = 1 506 + 1;
• 1 506 ÷ 2 = 753 + 0;
• 753 ÷ 2 = 376 + 1;
• 376 ÷ 2 = 188 + 0;
• 188 ÷ 2 = 94 + 0;
• 94 ÷ 2 = 47 + 0;
• 47 ÷ 2 = 23 + 1;
• 23 ÷ 2 = 11 + 1;
• 11 ÷ 2 = 5 + 1;
• 5 ÷ 2 = 2 + 1;
• 2 ÷ 2 = 1 + 0;
• 1 ÷ 2 = 0 + 1;

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

 101,111,001,100 = 0000 0000 0000 0000 0000 0000 0001 0111 1000 1010 1010 1111 0111 0000 0000 1100 Apr 18 22:22 UTC (GMT) 1,302 = 0000 0101 0001 0110 Apr 18 22:21 UTC (GMT) -14,551 = 1011 1000 1101 0111 Apr 18 22:21 UTC (GMT) -5,050 = 1001 0011 1011 1010 Apr 18 22:20 UTC (GMT) -199 = 1000 0000 1100 0111 Apr 18 22:18 UTC (GMT) -10,355 = 1010 1000 0111 0011 Apr 18 22:17 UTC (GMT) 3 = 0011 Apr 18 22:15 UTC (GMT) -61 = 1011 1101 Apr 18 22:12 UTC (GMT) -3,456 = 1000 1101 1000 0000 Apr 18 22:12 UTC (GMT) -3,000 = 1000 1011 1011 1000 Apr 18 22:11 UTC (GMT) 107 = 0110 1011 Apr 18 22:08 UTC (GMT) -2,501 = 1000 1001 1100 0101 Apr 18 22:05 UTC (GMT) -2,113 = 1000 1000 0100 0001 Apr 18 22:05 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