Convert the Signed Integer Number 271 362 650 271 888 to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer Number as a Signed Binary Code (Written in Base Two). Detailed Explanations

Signed integer number 271 362 650 271 887 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

Signed integer number 271 362 650 271 889 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

How to convert a base ten signed integer number to signed binary:

1) Divide the positive version of the number repeatedly by 2, keeping track of each remainder. Stop when getting a quotient that is 0.

2) Construct the base two representation by taking the previously calculated remainders starting from the last remainder up to the first one.

3) Construct the positive binary computer representation so that the first bit is 0.

4) Only if the initial number is negative, change the first bit (the leftmost), from 0 to 1. The leftmost bit is reserved for the sign, 1 = negative, 0 = positive.

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

Conversions Between Decimal System Numbers (Written in Base Ten) and Binary System Numbers (Base Two and Computer Representation):

1. Integer -> Binary

• 1.1. Unsigned integer -> Unsigned binary

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  1.2. Signed integer -> Signed binary

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  1.3. Signed integer -> Signed binary one's complement

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  1.4. Signed integer -> Signed binary two's complement

2. Decimal -> Binary

• 2.1. Decimal -> 32bit single precision IEEE 754 binary floating point

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  2.2. Decimal -> 64bit double precision IEEE 754 binary floating point

3. Binary -> Integer

• 3.1. Unsigned binary -> Unsigned integer

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  3.2. Signed binary -> Signed integer

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  3.3. Signed binary one's complement -> Signed integer

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  3.4. Signed binary two's complement -> Signed integer

4. Binary -> Decimal

• 4.1. 32bit single precision IEEE 754 binary floating point -> Float

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  4.2. 64bit double precision IEEE 754 binary floating point -> Double