Question

Convert the decimal number 164 into the equivalent 8 bit binary number. ​

Answer 1

Answer:

10100100

Explanation:

8 bit system consists of 8 bits or 8 positions and each of them can have binary value (0 or 1).

Each bit is equivalent to a certain power of number 2. Important to know is that you read these bits from right to left.

So, this means that the bit furthest to the right has the value of 2^0, which is 1. The bit to the left has the value of 2^1, which is 2. Next one is 2^2, which is 4 etc. This means that the bit furthest to the left has the value of 2^7, which is 128.

The bit has this potential value only if value 1 if is in its position. If the value is 0 then, regardless of position, value of the bit is 0.

Decimal value of the number is calculated when we add all the values of the bits marked with 1.

So, we're dealing with number 164. We already said that leftmost bit has the value of 128 if it's marked with 1:

1 0 0 0 0 0 0 0 = 128

Next bit has the value of 64, but 128+64 would exceed the value of our number, so the second leftmost bit remains 0.

Next bit has the value of 32, 128+32 is 160, which is less then our number, so we mark the third bit with 1:

1 0 1 0 0 0 0 0 = 160

Similarly, we continue down the line. We only need 4 to reach the value of our number, so we'll mark with 1 the bit that has the value of 4, which leaves us with the solution:

1 0 1 0 0 1 0 0 = 164