Answer:
Adding another bit to a binary number will expand the maximum value that can be represented by that number by a power of 2. Examples: 1111 can store 15 in decimal, while 11111 can store 31 in decimal.
Adding a bit to a binary number is exactly the same as adding a "place" to a binary number and will expand the range of values that can be represented by an order of magnitude.
Step-by-step explanation:
A single bit can only be used to represent 1 or 0. But if you add a second bit, you can now represent numbers up to 3. Each new binary digit added to a binary number adds another power of 2 (binary is based on 2 states, on/off or 1 and 0) at that position. Look at this comparison of digits and their associated maximum number between a binary (base 2 number) vs. a decimal number (base 10 numbers that you use every day).
Digits Max Binary Max Decimal
1 1 1
2 11 (3) 99
3 111 (7) 999
4 1111 (15) 9,999
5 11111 (31) 99,999
6 111111 (63) 999,999
7 1111111 (127) 9,999,999
8 11111111 (255) 99,999,999
As you can see, each time we add a new digit in binary we expand the maximum number by 2x (actually 2x-1). When we add another digit to a decimal number we expand the maximum number by 10x (actually 10x-1).