1 / 15

ECE 103 Engineering Programming Chapter 3 Numbers

ECE 103 Engineering Programming Chapter 3 Numbers. Herbert G. Mayer, PSU CS Status 6/21/2014 Initial content copied verbatim from ECE 103 material developed by Professor Phillip Wong @ PSU ECE. Syllabus. What’s This Blue Code? Binary Numbers Number Conversion Decimal - Binary

Download Presentation

ECE 103 Engineering Programming Chapter 3 Numbers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. ECE 103 Engineering ProgrammingChapter 3Numbers Herbert G. Mayer, PSU CS Status 6/21/2014 Initial content copied verbatim from ECE 103 material developed by Professor Phillip Wong @ PSU ECE

  2. Syllabus • What’s This Blue Code? • Binary Numbers • Number Conversion Decimal - Binary • Bitwise Operations • Logic Operations • Other Base Representations • Convert Decimal to Hex • Positive and Negative Integers • Floating Point Numbers

  3. What’s This Blue Code? void foo( void ) { // foo } //end foo // <- implied return here int main( /* no params */ ) { // main foo(); return 0; // says: nothing went wrong! } //end main // learned about: Functions // similar to the printf() which you saw earlier

  4. Binary Numbers Bit  Smallest unit of information(binary digit) A single bit has two distinct states: 0 (logical False, power close to 0 V 1 logical True, power close to defined + V A binary number consists of n bitsgrouped together. LSB MSB bn-1bn-2…b1b0 = bn-12n-1 + bn-22n-2 + … + b121 + b020 3

  5. Binary Numbers Table 1: Given n bits, the number of possible states = 2n 4

  6. Number Conversion Decimal - Binary Convert from binary to its equivalent base 10 value Expand the powers of two Example: What is 11102in decimal? 11102 = (123) + (122) + (121) + (020) = (18) + (14) + (12) + (01) = 1410 Convert from base 10 to its equivalent binary value Successively divide by two; keep track of remainders Example: What is 1410 in binary? Read the remainders backwards. Hence, 1410 = 11102 5

  7. Bitwise Operations Bitwise Complement Bitwise AND Bitwise OR Bitwise XOR Bitwise Addition 6

  8. Logic Operations Logic operations are done one bit at a time (unary, AKA monadic) or a pair of bits (binary, AKA dyadic) Example: ~1011 = 0100 Complement, unary 1010 & 1100 = 1000 Bitwise AND, binary 1010 | 1100 = 1110 Bitwise OR 1010 ^ 1100 = 0110 Bitwise XOR 7

  9. Other Base Representations Octal (base 8  0, …, 7) Hexadecimal (base 16  0, …, 9, A, B, C, D, E, F with F representing 1510) Table 2: 4-bit positive integer conversion table 8

  10. Convert Binary to Hex Converting from binary to its equivalent hex:1) Separate binary value into 4-bit groups2) Replace each group by its hex value Example: 4410010 = 10101100010001002 = AC4416 Converting from hex to its equivalent binary:Replace each hex value by its 4-bit binary value. Example: 2741110 = 6B1316 = 01101011000100112 9

  11. Positive and Negative Integers Integers are exactly representable in base 2 Table 3: 4-bit positive only values 0 to 15 If only positive integers and zero are needed, then all of the bits in the binary representation are available to express the value. Given : n bits Range: 0 to 2n – 1 10

  12. For negative integers, the most significant bit (MSB) of the binary value is reserved as a sign bit Negative values are expressed as 2’s complement Table 4: 4-bit positive and negative values -8 to +7 If both positive and negative integers are needed, the maximum positive value is reduced by a factor of 2 Given : n bits Range: –2n-1 to 2n-1 – 1 11

  13. Floating Point Numbers God created integers; Man invented floats Floating point is used to express real-valued numbers. There is an implicit base and decimal point Example: 2.0 3.1415 –634.9 Example: In scientific notation format (base 10) –6.349 × 102 mantissa exponent sign base 12

  14. Binary can be used to represent floating point values, but usually only as an approximation IEEE 754single-precision (32-bit) standard s e1e2…e8 b1b2…b23 8 bits Interpreted as unsigned integer e' 1 bit Sign 0→+ 1→– 23 bits Interpreted as a base 2 value defined as m' =0.b1b2…b23 = b12-1 + b22-2 +…+ b232-23 if e'≠ 0 then FP number = (-1)s × (1 + m') × 2e'-127 if e' = 0 then FP number = (-1)s × m'× 2-126 13

  15. Example: IEEE 754 single precision (32-bit) 01010110010010100000000000000000 The more bits available, the more precise the mantissa and the larger the exponent range Number = (-1)s × (1 + m') × 2e'-127 = 1.578125 × 245≈ 5.55253372027 × 1013 s = 0 m' = 2-1 + 2-4 + 2-6 = 0.578125 e' = 17210 14

More Related