# Signed: Integer ↗ Binary: 97 880 266 497 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 97 880 266 497(10)converted and written as a signed binary (base 2) = ?

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

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

• division = quotient + remainder;
• 97 880 266 497 ÷ 2 = 48 940 133 248 + 1;
• 48 940 133 248 ÷ 2 = 24 470 066 624 + 0;
• 24 470 066 624 ÷ 2 = 12 235 033 312 + 0;
• 12 235 033 312 ÷ 2 = 6 117 516 656 + 0;
• 6 117 516 656 ÷ 2 = 3 058 758 328 + 0;
• 3 058 758 328 ÷ 2 = 1 529 379 164 + 0;
• 1 529 379 164 ÷ 2 = 764 689 582 + 0;
• 764 689 582 ÷ 2 = 382 344 791 + 0;
• 382 344 791 ÷ 2 = 191 172 395 + 1;
• 191 172 395 ÷ 2 = 95 586 197 + 1;
• 95 586 197 ÷ 2 = 47 793 098 + 1;
• 47 793 098 ÷ 2 = 23 896 549 + 0;
• 23 896 549 ÷ 2 = 11 948 274 + 1;
• 11 948 274 ÷ 2 = 5 974 137 + 0;
• 5 974 137 ÷ 2 = 2 987 068 + 1;
• 2 987 068 ÷ 2 = 1 493 534 + 0;
• 1 493 534 ÷ 2 = 746 767 + 0;
• 746 767 ÷ 2 = 373 383 + 1;
• 373 383 ÷ 2 = 186 691 + 1;
• 186 691 ÷ 2 = 93 345 + 1;
• 93 345 ÷ 2 = 46 672 + 1;
• 46 672 ÷ 2 = 23 336 + 0;
• 23 336 ÷ 2 = 11 668 + 0;
• 11 668 ÷ 2 = 5 834 + 0;
• 5 834 ÷ 2 = 2 917 + 0;
• 2 917 ÷ 2 = 1 458 + 1;
• 1 458 ÷ 2 = 729 + 0;
• 729 ÷ 2 = 364 + 1;
• 364 ÷ 2 = 182 + 0;
• 182 ÷ 2 = 91 + 0;
• 91 ÷ 2 = 45 + 1;
• 45 ÷ 2 = 22 + 1;
• 22 ÷ 2 = 11 + 0;
• 11 ÷ 2 = 5 + 1;
• 5 ÷ 2 = 2 + 1;
• 2 ÷ 2 = 1 + 0;
• 1 ÷ 2 = 0 + 1;

## 97 880 266 497(10) = 0000 0000 0000 0000 0000 0000 0001 0110 1100 1010 0001 1110 0101 0111 0000 0001

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

## 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
• Number -63(10), signed integer, converted from decimal system (base 10) to signed binary = 1011 1111