Question

How many bits are required to represent the following decimal numbers as unsigned binary integers?

a) 12
b) 147
c) 384
d) 1497
e) 2048

Answer 1

To find the number of bits needed for unsigned binary representation, the next power of 2 greater than or equal to the number is determined. For example, 12 requires 4 bits, 147 requires 8 bits, 384 needs 9 bits, 1497 uses 12 bits, and 2048 needs 11 bits.

Step-by-step explanation:

To determine how many bits are required to represent a given decimal number as an unsigned binary integer, one must find the smallest power of 2 that is equal to or greater than the number. Here are the calculations for the provided numbers:

• 12 can be represented as 1100 in binary, which is 4 bits.
• 147 can be represented as 10010011 in binary, which is 8 bits.
• 384 can be represented as 110000000 in binary, which is 9 bits.
• 1497 can be represented as 10111011001 in binary, which requires 12 bits.
• 2048 is exactly 211, so it can be represented as 1 followed by eleven 0s in binary, which is 11 bits.

Remember, the general process to determine the number of bits is to find the next power of 2 that is greater than or equal to the number and count the number of powers.