1. Digital Systems and Information Dr. Sanjay P. Ahuja, Ph.D. FIS Distinguished Professor of CIS (2010-2014) School of Computing, UNF

2. Digital Systems and Information The computer is a digital system. It manipulates discrete elements of information from the set {0, 1}. Discrete information is represented in a digital system by signals. These signals use two discrete values and therefore are said to be binary signals (0 or 1, H or L, T or F). The two discrete values are represented by voltage ranges called HIGH and LOW.

3. Voltage Ranges for Binary Signals Input ranges are larger than output ranges to allow circuits to function correctly, i.e. recognize logics 1 and 0, in spite of variations in voltages due to “noise” voltages that may be added/subtracted from the output voltages.

4. Information Representation Digital computers use the binary number system, which has two digits, 0 and 1. A binary digit is called a bit. Example: (1001) 2 represents 9, i.e. 1 x 2 3 + 0 x 2 2 + 0 x 2 1 + 1 x2 0 = 9

5. Computer System A computer system is composed of hardware and system software. The hardware is divided into 3 parts: CPU, main memory, I/O devices. Central Processing Unit (CPU) comprises the Arithmetic and Logic Unit (ALU), registers, control unit (CU), and cache memory (L1 and L2 caches). Main memory, also called RAM stores instructions and data. The I/O interface or I/O cards such as graphics cards, Network interface cards (NICs) etc., contain circuits for communicating with and controlling the transfer of information between the computer and the outside world.

6. Binary Number System Allowed binary digits (bits) are 0 and 1 and the radix or base = 2. With 2 bits, we get 2 2 = 4 combinations: 00, 01, 10, 11. With n-bits, we get 2 n combinations. With 2 3, we have 8 combinations: MSB000 LSB 001 010 011 100 101 110 111

7. Base Conversion – Powers of 2

8. Special Powers of 2

9. Hexadecimal Number System A major numbering system used in digital systems is the hexadecimal system, also named base 16. In this system, the numbers are counted from 0 to 9 and, since in base 16 we need 16 different symbols, decimal numbers 10 through 15 are represented by letters A through F, respectively. So we go from 0-9, and A-F.