QMS 102 Lecture Notes - Lecture 18: Radix Point, Decimal Mark, Octal
12 May 2018
School
Department
Course
Professor
ITM 207 – Winter 2018
CH 1: Number Systems:
- Decimal numeric system:
o Have digits and a base
o 48. 4,8. 4x10^1 (weight of specific digit. So, 10. Exponent is digit position of 10) +
8x10^0
o 4 is most significant digit – most weight
o 8 is least significant digit – least weight
o These are integers
o Digits in DNS: 0,1,2,3,4,5,6,7,8,9
o Base: 10
- Binary numeric system:
o Called bits
o MSD or Most significant bit
o LSD or Least significant bit
o Digits: 0,1
o Base: 2
o EX. 101
o 2
o 0,1 are digits (two ones)
o LSD: 1x2^0
o MSD: 1x2^2
o =5
o EX. 1100
o 2
o Digits: 0,1
o LSD: 0x2^0
o MSD: 1x2^3
o =12
o 8
o 10
o =?2
o 8/2=4. 8/8=0
o 4/2=2. 4/4=0
o 2/2=1. 2/2=0
o 1= MSD
o =1001
o 2
- Octal numeric system:
o Base: 8
o Digits: 0,1,2,3,4,5,6,7
o 10
o 8
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o ex. 17
o 8
o 1x8^1 + 7x8^0
o 8+7=15
o 15
o 10
o =?8
o 15/8=1
o 15-8=7
o =17
o 8
- Representing negative values:
o Signed magnitude number representation:
▪ Used by humans
▪ The sign represents the ordering (the negatives come before the positives
in ascending order)
▪ The digits represent the magnitude (the distance from zero)
- Representing real numbers:
o Real numbers are with a whole part and a fractional part (either of which may be
zero)
o 104.32
o 0.99999
o 357.0
o 3.14159
o In decimals, positions to the right of the decimal point are the tenths,
hundredths, thousandths, etc.
o Same rule applies in binary as in decimal
▪ Radix point is geeal te fo deial poit
▪ Positions to the right of the radix point in binary:
• 2^-1 = halves position
• 2^-2 = quarters position
• 2^-3 = eights position
o A real value in base 10 can be defined by the following formula where the
mantissa is an integer
▪ Sign * mantissa * 10^exp
o This representation is called floating point eause the adi poit floats
o In analogy to the fixed numbers of bits that computers use to represent integers,
e’ll teat the atissa as haig a fied ue of digits
o Scientific notation:
▪ A form of floating-point representation in which the decimal point is kept
to the right of the leftmost digit
- Character set:
o A list of characters and the codes used to represent each one
- The ASCII Character set:
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Document Summary
Decimal numeric system: have digits and a base, 48. 8x10^0: 4 is most significant digit most weight, 8 is least significant digit least weight, these are integers, digits in dns: 0,1,2,3,4,5,6,7,8,9, base: 10. Binary numeric system: called bits, msd or most significant bit, lsd or least significant bit, digits: 0,1, base: 2, ex. 2: 0,1 are digits (two ones, lsd: 1x2^0, msd: 1x2^2, =5, ex. 2: digits: 0,1, lsd: 0x2^0, msd: 1x2^3, =12, 8. Octal numeric system: base: 8, digits: 0,1,2,3,4,5,6,7, 10. Representing negative values: signed magnitude number representation, used by humans, the sign represents the ordering (the negatives come before the positives in ascending order, the digits represent the magnitude (the distance from zero) Representing real numbers: real numbers are with a whole part and a fractional part (either of which may be zero, 104. 32, 0. 99999, 357. 0, 3. 14159. Character set: to the right of the leftmost digit: a list of characters and the codes used to represent each one.
