What is the largest decimal integer that can be represented with the following number of bits? 1. 3 bits 2. 8 bits 3. 32 bits 4. 64 bits How do you find out the largest decimal integer? Solution In general, with k bits we can represent 2k values. Their range will depend on the system: Unsigned: 0 to 2k-1 1. 3 bits => 2^3 - 1 => 7 => 111 2. 8 bits => 2^8 - 1 => 255 3. 32 bits => 2^32 - 1 4. 64 bits => 2^64 - 1.

1. What is the largest decimal integer that can be represented with the following number of bits?
1. 3 bits
2. 8 bits
3. 32 bits
4. 64 bits
How do you find out the largest decimal integer?
Solution
In general, with k bits we can represent 2k values. Their range will depend on the system:
Unsigned: 0 to 2k-1
1. 3 bits
=> 2^3 - 1 => 7 => 111
2. 8 bits
=> 2^8 - 1 => 255
3. 32 bits
=> 2^32 - 1
4. 64 bits
=> 2^64 - 1