1’s in a row, e.g., 10101, which are equal to a sum of a series of powers of
two, as opposed to decimal numbers that are expressed in powers of 10.
Thus, the binary number 10101 is equal to the decimal number (1 × 24 +
0 × 23 + 1 × 22 + 0 × 21 + 1 × 20 ) =21, which is given as 2 × 101 + 1 × 100
in the decimal system.
The bits, 1 and 0, are represented by the “on” or “off” states of many tran-
sistor components present in the computer memory. A two-bit number can
be expressed in 2^2 , or four, ways (00, 01, 10, 11) corresponding to decimal
numbers, 0, 1, 2, 3; a three-bit number can be expressed in 2^3 , or eight, ways
(000, 001, 010, 011, 100, 101, 110, 111) corresponding to decimal numbers 0,
1,2,...7,and an n-bit number can be expressed in 2nways corresponding
to decimal numbers from 0 to 2n−1. In computer nomenclature, a byteof
memory is equal to eight bits that can store up to 2^8 , i.e., 0 to 255, units of
information. Similarly, a wordof memory consists of 16 bits or two bytes
and can store up to 2^16 , i.e., 0 to 65,535, units of information. In newer com-
puters, a word can consist of 32 or 64 bits, allowing more counts to be stored
in memory.
Central Processing Unit
The CPU, also called the microprocessor, performs all control, logic, and
arithmetic operations in a computer. A computer program is a set of
sequential instructions for the computer to perform with essential data
inserted whenever appropriate. The CPU retrieves the instructions and data
140 11. Digital Computers in Nuclear Medicine
Fig. 11.1. Basic components of a computer.