Tell me how to convert numbers from binary to decimal and vice versa.
Binary to Decimal:
1) Write down the number in expanded form;
2) Calculate.
Example: 0111.01 needs to be converted to decimal notation. To do this, we first have to arrange the digits, starting with the digit in front of the comma. Then you need to multiply the number by two to the power of the given number. I will now show the record of this example in expanded form to make it clearer: 0 * 2 ^ 3 + 1 * 2 ^ 2 + 1 * 2 ^ 1 + 1 * 2 ^ 0 + 0 * 2 ^ (- 1). Now you need to calculate everything. The answer would be: 7.25.
Decimal to Binary:
1) Consecutively perform division by two until we get an incomplete quotient less than the divisor;
2) The resulting residues are the numbers of the new system;
3) Make up a number by writing it down from the last remainder.
Example: 75 needs to be converted to binary. We sequentially divide it by two, getting the remainders: 75: 2 = 37 (remain. 1), 37: 2 = 18 (remain. 1), 18: 2 = 9 (remain. 0), 9: 2 = 4 (remain . 1), 4: 2 = 2 (rest 0), 2: 2 = 1 (rest 0). Answer: 001011.