# Signed: Integer -> Binary: -4 611 686 018 427 388 003 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

## Signed integer number -4 611 686 018 427 388 003(10)converted and written as a signed binary (base 2) = ?

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

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

• division = quotient + remainder;
• 4 611 686 018 427 388 003 ÷ 2 = 2 305 843 009 213 694 001 + 1;
• 2 305 843 009 213 694 001 ÷ 2 = 1 152 921 504 606 847 000 + 1;
• 1 152 921 504 606 847 000 ÷ 2 = 576 460 752 303 423 500 + 0;
• 576 460 752 303 423 500 ÷ 2 = 288 230 376 151 711 750 + 0;
• 288 230 376 151 711 750 ÷ 2 = 144 115 188 075 855 875 + 0;
• 144 115 188 075 855 875 ÷ 2 = 72 057 594 037 927 937 + 1;
• 72 057 594 037 927 937 ÷ 2 = 36 028 797 018 963 968 + 1;
• 36 028 797 018 963 968 ÷ 2 = 18 014 398 509 481 984 + 0;
• 18 014 398 509 481 984 ÷ 2 = 9 007 199 254 740 992 + 0;
• 9 007 199 254 740 992 ÷ 2 = 4 503 599 627 370 496 + 0;
• 4 503 599 627 370 496 ÷ 2 = 2 251 799 813 685 248 + 0;
• 2 251 799 813 685 248 ÷ 2 = 1 125 899 906 842 624 + 0;
• 1 125 899 906 842 624 ÷ 2 = 562 949 953 421 312 + 0;
• 562 949 953 421 312 ÷ 2 = 281 474 976 710 656 + 0;
• 281 474 976 710 656 ÷ 2 = 140 737 488 355 328 + 0;
• 140 737 488 355 328 ÷ 2 = 70 368 744 177 664 + 0;
• 70 368 744 177 664 ÷ 2 = 35 184 372 088 832 + 0;
• 35 184 372 088 832 ÷ 2 = 17 592 186 044 416 + 0;
• 17 592 186 044 416 ÷ 2 = 8 796 093 022 208 + 0;
• 8 796 093 022 208 ÷ 2 = 4 398 046 511 104 + 0;
• 4 398 046 511 104 ÷ 2 = 2 199 023 255 552 + 0;
• 2 199 023 255 552 ÷ 2 = 1 099 511 627 776 + 0;
• 1 099 511 627 776 ÷ 2 = 549 755 813 888 + 0;
• 549 755 813 888 ÷ 2 = 274 877 906 944 + 0;
• 274 877 906 944 ÷ 2 = 137 438 953 472 + 0;
• 137 438 953 472 ÷ 2 = 68 719 476 736 + 0;
• 68 719 476 736 ÷ 2 = 34 359 738 368 + 0;
• 34 359 738 368 ÷ 2 = 17 179 869 184 + 0;
• 17 179 869 184 ÷ 2 = 8 589 934 592 + 0;
• 8 589 934 592 ÷ 2 = 4 294 967 296 + 0;
• 4 294 967 296 ÷ 2 = 2 147 483 648 + 0;
• 2 147 483 648 ÷ 2 = 1 073 741 824 + 0;
• 1 073 741 824 ÷ 2 = 536 870 912 + 0;
• 536 870 912 ÷ 2 = 268 435 456 + 0;
• 268 435 456 ÷ 2 = 134 217 728 + 0;
• 134 217 728 ÷ 2 = 67 108 864 + 0;
• 67 108 864 ÷ 2 = 33 554 432 + 0;
• 33 554 432 ÷ 2 = 16 777 216 + 0;
• 16 777 216 ÷ 2 = 8 388 608 + 0;
• 8 388 608 ÷ 2 = 4 194 304 + 0;
• 4 194 304 ÷ 2 = 2 097 152 + 0;
• 2 097 152 ÷ 2 = 1 048 576 + 0;
• 1 048 576 ÷ 2 = 524 288 + 0;
• 524 288 ÷ 2 = 262 144 + 0;
• 262 144 ÷ 2 = 131 072 + 0;
• 131 072 ÷ 2 = 65 536 + 0;
• 65 536 ÷ 2 = 32 768 + 0;
• 32 768 ÷ 2 = 16 384 + 0;
• 16 384 ÷ 2 = 8 192 + 0;
• 8 192 ÷ 2 = 4 096 + 0;
• 4 096 ÷ 2 = 2 048 + 0;
• 2 048 ÷ 2 = 1 024 + 0;
• 1 024 ÷ 2 = 512 + 0;
• 512 ÷ 2 = 256 + 0;
• 256 ÷ 2 = 128 + 0;
• 128 ÷ 2 = 64 + 0;
• 64 ÷ 2 = 32 + 0;
• 32 ÷ 2 = 16 + 0;
• 16 ÷ 2 = 8 + 0;
• 8 ÷ 2 = 4 + 0;
• 4 ÷ 2 = 2 + 0;
• 2 ÷ 2 = 1 + 0;
• 1 ÷ 2 = 0 + 1;

## 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