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COMPUTER NUMBER SYSTEMS & DIGITAL DEVICES By: Sohaib Rehman

COMPUTER NUMBER SYSTEMS & DIGITAL DEVICES By: Sohaib Rehman. Number System & Digital Devices. To understand the structure of the binary number system, first step is to review the decimal or base-10 number system. Example 5 3 4 6 . 7 2 10 3 10 2 10 1 10 0 10 -1 10 -2

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COMPUTER NUMBER SYSTEMS & DIGITAL DEVICES By: Sohaib Rehman

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  1. COMPUTER NUMBER SYSTEMS & DIGITAL DEVICESBy: SohaibRehman

  2. Number System & Digital Devices • To understand the structure of the binary number system, first step is to review the decimal or base-10 number system. • Example 5 3 4 6 . 7 2 103 102 101 100 10-1 10-2 • This tells you that you have 5 thousands, 3 hundreds, 4 tens, 6 ones, 7 tenths and 2 hundredths.

  3. Binary Number System • In a binary number system, each digit represents a power of 2. • A binary digit is often called a BIT. • The binary system uses only two numbers i.e. 1 & 0. • Example of binary number system is 1 0 1 1 0 . 1 1 24 23 22 21 20 2-1 2-2

  4. Binary Number System • To convert a binary number into its equivalent decimal number, multiply each digit times the decimal value of the digit and just add these up. • The binary number 101, represents (1 * 22) + (0 * 21) + (1 * 20) 4 + 0 + 1 = 5 ( Decimal) • What is the decimal equivalent for 10110.11 ?

  5. Binary Conversion • 22710 = ? • 10910 = ? • Conversion from decimal to binary is a simple method and is a part of a class exercise.

  6. Hexadecimal • Computer require binary digits, so why use hexadecimal? • Example shows the digit values for hexadecimal which is often called hex. 162 161 160 . 16-1 16-2 256 16 1 1/16 1/256

  7. Hexadecimal Dec Hex Dec Hex 0 = 0 8 = 8 1 = 1 9 = 9 2 = 2 10 = A 3 = 3 11 = B 4 = 4 12 = C 5 = 5 13 = D 6 = 6 14 = E 7 = 7 15 = F

  8. Binary-Coded Decimals • In applications such as frequency counters, digital voltmeters, or calculators, where the output is a decimal display, a BCD code is often used. • BCD uses a 4-bit binary code to represent each decimal digit in a number. • The simplest BCD code uses the first 10 numbers of standard binary code for the BCD numbers 0 through 9.

  9. Binary-Coded Decimals • The Hexadecimals codes A through F are invalid BCD codes. • To convert a decimal number to its BCD equivalent, just represent each decimal digit by its 4-bit binary equivalent. • Example of BCD Decimal 5 2 9 BCD 0101 0010 1001

  10. Gray Code • Gray Code is another important binary code. • It is often used for encoding shaft position data from machines such as computer controlled latches. • Only one binary digit changes at a time as you count up in this code. • Example Binary 0000 0001 0010 0011 0100 Gray 0000 0001 0011 0010 0110

  11. Gray Code

  12. Basic Digital Devices • Inverting & non-inverting buffers. • Logic Gates. • Programmable logic Devices ( PLD’s ). • PLA’s • PROM’s.

  13. Basic Digital Devices • Latches • Flip Flops • Registers • Counters • ROM • RAM • Buses • ALU.

  14. Reading Assignment • Binary, Decimal, Octal, Hexa Decimal number systems with their conversion and addition, subtraction, multiplication, division and digital devices.

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