NCERT Solutions for Class 9th Maths Chapter 1 Number Systems Exercise 1.3 Question 6<\/p>\n
Number Systems<\/p>\n
Decimal<\/p>\n
Here\u2019s the decimal number system as an example:
\ndigits (or symbols) allowed: 0-9
\nbase (or radix): 10
\nthe order of the digits is significant<\/p>\n
345 is really
\n3 x 100 + 4 x 10 + 5 x 1
\n3 x 10^2 + 4 x 10^1 + 5 x 10^0
\n3 is the most significant symbol (it carries the most weight)
\n5 is the least significant symbol (it carries the least weight)
\nBinary<\/p>\n
Here\u2019s a binary number system:
\ndigits (symbols) allowed: 0, 1
\nbase (radix): 2<\/p>\n
each binary digit is called a BIT<\/p>\n
the order of the digits is significant<\/p>\n
numbering of the digits
\nmsb lsb
\nn-1 0
\nwhere n is the number of digits in the number<\/p>\n
msb stands for most significant bit
\nlsb stands for least significant bit<\/p>\n
1001 (base 2) is really
\n1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0
\n9 (base 10)<\/p>\n
11000 (base 2) is really
\n1 x 2^4 + 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0
\n24 (base 10)<\/p>\n
Of interest: most assembly languages have no way to represent
\nbinary values!
\nOctal<\/p>\n
Here\u2019s an octal number system:
\ndigits (symbols) allowed: 0-7
\nbase (radix): 8<\/p>\n
the order of the digits is significant<\/p>\n
345 (base 8) is really
\n3 x 8^2 + 4 x 8^1 + 5 x 8^0
\n192 + 32 + 5
\n229 (base 10)<\/p>\n
1001 (base 8) is really
\n1 x 8^3 + 0 x 8^2 + 0 x 8^1 + 1 x 8^0
\n512 + 0 + 0 + 1
\n513 (base 10)<\/p>\n
Hexadecimal<\/p>\n
here\u2019s a hexadecimal number system:
\ndigits (symbols) allowed: 0-9, a-f
\nbase (radix): 16<\/p>\n
the order of the digits is significant<\/p>\n
hex decimal binary
\n0 0 0000
\n1 1 0001
\n.
\n.
\n.
\n9 9 1001
\na 10 1010
\nb 11 1011
\nc 12 1100
\nd 13 1101
\ne 14 1110
\nf 15 1111<\/p>\n
a3 (base 16) is really
\na x 16^1 + 3 x 16^0
\n160 + 3
\n163 (base 10)<\/p>\n","protected":false},"excerpt":{"rendered":"
NCERT Solutions for Class 9th Maths Chapter 1 Number Systems Exercise 1.3 Question 6 Number Systems Decimal Here\u2019s the decimal […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"\"Get NCERT Solutions for Class 9th Maths Chapter 1 Number Systems Exercise 1.3 Question 6 on Infinity Learn.\"","custom_permalink":"ncert-solutions\/class-9th\/maths\/ncert-solutions-for-class-9th-maths-chapter-1-number-systems-exercise-1-3-question-6\/"},"categories":[13,54,71],"tags":[],"table_tags":[],"acf":[],"yoast_head":"\n