Convert the base-10 number 74 into an 8-bit binary number

In base-10 (denary) representation numbers are represented by saying how many units, tens, hundreds, thousands etc... there are from right to left. So for 74 there are 7 tens and 4 units. In binary, each digit (read from right to left) is a power of 2 starting from the 0th power i.e. the first digit is 2^0 (1), the second digit is 2^1 (2), third digit 2^2 (4) and so on. For 8-bit binary the largest digit can be of 2^7 (128). Furthermore, in binary, you can only ever have 1 or 0 of each digit. Now to convert from denary 74 to binary we start by seeing if the 2^7 bit which is 128 can go into 74. It can't so the 128 bit is 0. The next lowest bit is 2^6 = 64. 64 can go into 74 once so the 64 bit is 1. Now, the remainder of the number left to represent is found by subtracting 64 from 74 to give 10. Continuing to look at each bit in sequence comparing to the remainder 10: 2^5 bit = 32 does not go into 10 so is 0. 2^4 bit = 16 does not go into 10 so is 0. 2^3 bit = 8 does go into 10 so is 1 and the remainder to find is 10-8 = 2. 2^2 bit = 4 does not go into 2 so is 0. 2^1 bit =2 does go into 2 so is 1 and the remainder to find is 2-2 = 0. As we have nothing left tor represent the last remaining bit 2^0 = 1 is 0. Putting this altogether we can write the binary number as 01001010 which is the 8-bit binary representation of 74.