Base ten decimal system signed integer number -57 converted to signed binary in two's complement representation

How to convert a signed integer in decimal system (in base 10): -57(10) to a signed binary two's complement representation

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

• division = quotient + remainder;
• 57 ÷ 2 = 28 + 1;
• 28 ÷ 2 = 14 + 0;
• 14 ÷ 2 = 7 + 0;
• 7 ÷ 2 = 3 + 1;
• 3 ÷ 2 = 1 + 1;
• 1 ÷ 2 = 0 + 1;

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

 -57 = 1100 0111 Jun 24 15:16 UTC (GMT) 2,018 = 0000 0111 1110 0010 Jun 24 15:15 UTC (GMT) -2,016 = 1111 1000 0010 0000 Jun 24 15:15 UTC (GMT) 26,436 = 0110 0111 0100 0100 Jun 24 15:15 UTC (GMT) 11,010,011 = 0000 0000 1010 0111 1111 1111 1101 1011 Jun 24 15:14 UTC (GMT) -7,586 = 1110 0010 0101 1110 Jun 24 15:14 UTC (GMT) -113 = 1000 1111 Jun 24 15:14 UTC (GMT) -76 = 1011 0100 Jun 24 15:13 UTC (GMT) -48 = 1101 0000 Jun 24 15:13 UTC (GMT) -200 = 1111 1111 0011 1000 Jun 24 15:13 UTC (GMT) -980 = 1111 1100 0010 1100 Jun 24 15:10 UTC (GMT) -913 = 1111 1100 0110 1111 Jun 24 15:10 UTC (GMT) 42 = 0010 1010 Jun 24 15:09 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