FIT1047 Study Guide - Final Guide: Cyclic Redundancy Check, Checksum, Negative Number
31 May 2018
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Representing Numbers
Representing Numbers
• In computers, everything is represented by 0 and 1
• When we see a number (365), we use the decimal system to interpret it.
o We see 365 as 300 + 60 + 5
• Computers work with only two different symbols - high voltage and low voltage
o Sometimes defining power on and power off
o These are the 0 and 1's
Binary Numbers
• Similar to decimal system, but rather than being 10x as much for each position, it is 2x as much
• 101101101
o 2^8 + 0 + 2^6 + 2^5 + 0 + 2^3 + 2^2 + 0 + 2^0
o = 256 + 0 + 64 + 32 + 0 + 8 + 4 + 0 + 1
o = 365
• Addition:
o Same as decimal addition. 1 + 1 = 0 (with a carry of 1)
o 1101 + 11 = 1000
• Conversions
o Ex. 365
o Find largest power of 2 that is closest to 365. (2^8 = 256) 1xxxxxxxx
o 365 - 256 = 109. Find largest power of 2 that is closest to 109. (2^6 = 64). Add a 0 for the
2^7. 101xxxxxx
o Keep going until you reach 0
Bites, Bytes and Words
• A bit is a single binary digit (0 or 1)
• 8 bits is a byte
• A fixed width of a collection of bits is a word.
o Often 16, 32 or 64 bits
Hexadecimal Numbers
• Base 16
• 4 bits
• 0 - 9 is numbers. 10 - 15 is letters A to F
Text to Binary
• ASCII is most common encoding that computers use (7 bits)
• Assigns each possible character to a fixed bit
• Nowadays, ASCII is not enough for all characters of different languages. Hence UNICODE is
used. (32 bits)
• Each character corresponds to 32 bits. (Large amount of storage required)
• UTF-8 uses 8 bits per character
• UTF-16 uses 16 bits per character
Negative Binary Numbers
Sign and Magnitude
• Leftmost bit is sign. 0 for positive, 1 for negative. Rest of number is the actual number.
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Document Summary
1 + 1 = 0 (with a carry of 1: 1101 + 11 = 1000, conversions, ex. 365: find largest power of 2 that is closest to 365. (2^8 = 256) 1xxxxxxxx, 365 - 256 = 109. Find largest power of 2 that is closest to 109. (2^6 = 64). 101xxxxxx: keep going until you reach 0. Bites, bytes and words: a bit is a single binary digit (0 or 1, 8 bits is a byte, a fixed width of a collection of bits is a word, often 16, 32 or 64 bits. Hexadecimal numbers: base 16, 4 bits, 0 - 9 is numbers. 10 - 15 is letters a to f. Text to binary: ascii is most common encoding that computers use (7 bits, assigns each possible character to a fixed bit, nowadays, ascii is not enough for all characters of different languages.
