# Base ten decimal system signed integer number 4 097 converted to signed binary in two's complement representation

## How to convert a signed integer in decimal system (in base 10): 4 097(10) to a signed binary two's complement representation

### 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;
• 4 097 ÷ 2 = 2 048 + 1;
• 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;

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

 4,097 = 0001 0000 0000 0001 Oct 16 19:57 UTC (GMT) -256 = 1111 1111 0000 0000 Oct 16 19:57 UTC (GMT) -21 = 1110 1011 Oct 16 19:57 UTC (GMT) -26 = 1110 0110 Oct 16 19:57 UTC (GMT) -21 = 1110 1011 Oct 16 19:54 UTC (GMT) 102 = 0110 0110 Oct 16 19:54 UTC (GMT) -357,821 = 1111 1111 1111 1010 1000 1010 0100 0011 Oct 16 19:53 UTC (GMT) -2,130,705,662 = 1000 0001 0000 0000 0000 0011 0000 0010 Oct 16 19:53 UTC (GMT) -145 = 1111 1111 0110 1111 Oct 16 19:52 UTC (GMT) -145 = 1111 1111 0110 1111 Oct 16 19:52 UTC (GMT) -112 = 1001 0000 Oct 16 19:51 UTC (GMT) -153 = 1111 1111 0110 0111 Oct 16 19:51 UTC (GMT) -100,010 = 1111 1111 1111 1110 0111 1001 0101 0110 Oct 16 19:51 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