Base ten decimal system unsigned (positive) integer number 654 converted to unsigned binary (base two)

How to convert an unsigned (positive) integer in decimal system (in base 10): 654_{(10)} to an unsigned binary (base 2)

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;

654 ÷ 2 = 327 + 0;

327 ÷ 2 = 163 + 1;

163 ÷ 2 = 81 + 1;

81 ÷ 2 = 40 + 1;

40 ÷ 2 = 20 + 0;

20 ÷ 2 = 10 + 0;

10 ÷ 2 = 5 + 0;

5 ÷ 2 = 2 + 1;

2 ÷ 2 = 1 + 0;

1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:

654_{(10)} = 10 1000 1110_{(2)}

Conclusion:

Number 654_{(10)}, a positive integer (no sign), converted from decimal system (base 10) to an unsigned binary (base 2):

10 1000 1110_{(2)}

Spaces used to group numbers digits: for binary, by 4.

Convert positive integer numbers (unsigned) from the decimal system (base ten) to binary (base two)

How to convert a base ten positive integer number to base two:

1) Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is ZERO;

2) Construct the base 2 representation by taking all the previously calculated remainders starting from the last remainder up to the first one, in that order.

Latest positive integer numbers (unsigned) converted from decimal (base ten) to unsigned binary (base two)

How to convert unsigned integer numbers (positive) from decimal system (base 10) to binary = simply convert from base ten to base two

Follow the steps below to convert a base ten unsigned integer number to base two:

1. Divide repeatedly by 2 the positive integer number that has to be converted to binary, keeping track of each remainder, until we get a QUOTIENT that is equal to ZERO.

2. Construct the base 2 representation of the positive integer 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).

Example: convert the positive integer number 55 from decimal system (base ten) to binary code (base two):

1. Divide repeatedly 55 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:

division = quotient + remainder;

55 ÷ 2 = 27 + 1;

27 ÷ 2 = 13 + 1;

13 ÷ 2 = 6 + 1;

6 ÷ 2 = 3 + 0;

3 ÷ 2 = 1 + 1;

1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive integer number, by taking all the remainders starting from the bottom of the list constructed above: 55_{(10)} = 11 0111_{(2)}

Number 55_{10}, positive integer (no sign), converted from decimal system (base 10) to unsigned binary (base 2) = 11 0111_{(2)}