Number Systems Guide, Cheat Sheet of Computer science

The Number Systems Guide - Decimal, Binary, Hexadecimal, Octal

Typology: Cheat Sheet

2023/2024

Uploaded on 08/04/2024

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Name: Specialization: Computer Systems Servicing
Track and Strand: TVL-ICT Subject: CSS II
NUMBER SYSTEMS
Number systems are also called numeral systems. Number System is any notation that represents
numerals or numbers.
1. Decimal – Most common number system, the basic of how we count, as we know it. It has a base
or radix of 10.
2. Binary – Computer machine language. It means on the machine level, this is the only recognizable
data to the computer. It has base or radix of 2.
3. Octal – Group of binary digits intro groups of three called octets. Thus, 23 is equal to 8, deriving the
name octal. 8 is its radix or base, represented by the symbols 0-7.
4. Hexadecimal – This number system is a spin off from octal system. It has a radix or base of 16.
DECIMAL
1 11 21 91 991 9991
2 12 22 92 992 9992
3 13 23 93 993 9993
4 14 24 94 994 9994
5 15 25 95 995 9995
6 16 26 96 996 9996
7 17 27 97 997 9997
8 18 28 98 998 9998
9 19 29 99 999 9999
10 20 30 100 1000 10000
84310 = (8 x 102) + (4 x 101) + (3 x 100)
= (8 x 100) + (4 x 10) + (3 x 1)
= 800 + 40 + 3
= 843
BINARY
OCTAL
Octal Decimal Octal Decimal
0 0 10 8
1 1 11 9
2 2 12 10
3 3 13 11
Base
2
Equivalen
t
Decimal Binary
201 0 0000
212 1 0001
224 2 0010
238 3 0011
2416 4 0100
2532 5 0101
2664 6 0110
27128 7 0111
28256 8 1000
29512 9 1001
2n
pf3

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Name: Specialization: Computer Systems Servicing Track and Strand: TVL-ICT Subject: CSS II

NUMBER SYSTEMS

Number systems are also called numeral systems. Number System is any notation that represents numerals or numbers.

  1. Decimal – Most common number system, the basic of how we count, as we know it. It has a base or radix of 10.
  2. Binary – Computer machine language. It means on the machine level, this is the only recognizable data to the computer. It has base or radix of 2.
  3. Octal – Group of binary digits intro groups of three called octets. Thus, 2^3 is equal to 8, deriving the name octal. 8 is its radix or base, represented by the symbols 0-7.
  4. Hexadecimal – This number system is a spin off from octal system. It has a radix or base of 16. DECIMAL 1 11 21 … 91 … 991 … 9991 2 12 22 … 92 … 992 … 9992 3 13 23 … 93 … 993 … 9993 4 14 24 … 94 … 994 … 9994 5 15 25 … 95 … 995 … 9995 6 16 26 … 96 … 996 … 9996 7 17 27 … 97 … 997 … 9997 8 18 28 … 98 … 998 … 9998 9 19 29 … 99 … 999 … 9999 10 20 30 … 100 … 1000 … 10000 84310 = (8 x 10^2 ) + (4 x 10^1 ) + (3 x 10^0 ) = (8 x 100) + (4 x 10) + (3 x 1) = 800 + 40 + 3 = 843 BINARY OCTAL Octal Decimal Octal Decimal 0 0 10 8 1 1 11 9 2 2 12 10 3 3 13 11 Base 2 Equivalen t Decimal Binary 20 1 0 0000 21 2 1 0001 22 4 2 0010 23 8 3 0011 24 16 4 0100 25 32 5 0101 26 64 6 0110 27 128 7 0111 28 256 8 1000 29 512 9 1001 2 n^ … … …

HEXADECIMAL

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

Decimal to Binary Conversion:

General rules in converting from a decimal number to any number system used in computing.

  1. Divide the decimal number by the base or radix of the number system you want to convert to.
  2. Write down the remainder of the division operation.
  3. Repeat steps (1) and (2) for each quotient you get until you cannot divide the quotient by the radix any further.
  4. Write down the remainder for each division operation in sequence from bottom to top to get the converted number. Decimal to Binary: Divide the Decimal number by radix/base “ 2 ”. Examples : Convert 166 10 to Binary 166 ÷ 2 = 83 remainder 0 83 ÷ 2 = 41 remainder 1 41 ÷ 2 = 20 remainder 1 20 ÷ 2 = 10 remainder 0 10 ÷ 2 = 5 remainder 0 5 ÷ 2 = 2 remainder 1 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Answer: 166 10 = 1010 0110 2 Convert 250 10 to Binary 250 ÷ 2 = 125 remainder 0 125 ÷ 2 = 62 remainder 1 62 ÷ 2 = 31 remainder 0 31 ÷ 2 = 15 remainder 1 15 ÷ 2 = 7 remainder 1 7 ÷ 2 = 3 remainder 1 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Answer: 250 10 = 1111 1010 2

Decimal to Octal Conversion:

General rules in converting from a decimal number to any number system used in computing.

  1. Divide the decimal number by the base or radix of the number system you want to convert to.
  2. Write down the remainder of the division operation.