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Number system is a system of representing numbers. In a number system, we can represent a number by its base. A base of 2 means it is a binary number, base of 8 means it is an octal number and if the base is 10 it is called the decimal number system. A base of 16 means it is a hexadecimal.<\/span><\/p>\n Decimal number system is used in various computer applications and is also called the base 10 number system. It consists of 10 digits from 0 to 9.\u00a0<\/span><\/p>\n In this number system every value has the place value of power 10 and can be written as:\u00a0<\/span><\/p>\n (82)_{10}=8 \\times 10^{1}+2 \\times 10^{0}<\/span><\/span><\/p>\n <\/span><\/p>\n The digits to the right side of the decimal point are written with their decreasing power of 10.<\/span><\/p>\n For example, if we have 125.6 then we can write it as:\u00a0<\/span><\/p>\n (125.6)_{10}=1 \\times 10^{2}+2 \\times 10^{1}+5 \\times 10^{0}+6 \\times 10^{-1}<\/span><\/span><\/p>\n <\/span><\/p>\n When we write a number, say 145.68, the number on the left side of the decimal point is read just like we would read in case of no decimal. Here, 145 = 100 + 40 + 5 which is one hundred forty five. The number to the right of the decimal is actually a number with decreasing power so 6 is actually 6-tenth and 8 is 8-hundredth. We read these numbers individually. We read the number 145.68 as <\/span>one hundred forty five point six eight.<\/b>\u00a0\u00a0<\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n 1. Converting Binary to Decimal<\/b><\/p>\n When we have binary numbers, which have the base 2, we can easily convert them to decimals with base 10.<\/span><\/p>\n Consider the number 1101_2<\/span><\/span>\u00a0which is a binary number. We have to convert it to a decimal number with base 10.\u00a0<\/span><\/p>\n We simply multiply the digits with decreasing power of 2 as follows-<\/span><\/p>\n 1 \\times 2^{3}+1 \\times 2^{2}+0 \\times 2^{1}+1 \\times 2^{0}<\/span><\/span><\/p>\n =8+4+0+1 <\/span><\/span><\/p>\n =13<\/span><\/span><\/p>\n Therefore,1101_{2}=13_{10}<\/span>.<\/span><\/p>\n <\/span><\/p>\n 2. Converting Octal to Decimal<\/b><\/p>\n Octal number has a base of 8. Every digit of the number is multiplied by the decreasing power of 8.\u00a0<\/span><\/p>\n Consider the number 112_{8}<\/span><\/span>which is an octal number. We will convert it to decimal number as follows \u2013\u00a0<\/span><\/p>\n 1 \\times 8^{2}+1 \\times 8^{1}+2 \\times 8^{0}<\/span><\/span><\/p>\n =64+8+2 <\/span> =74<\/span><\/span>\u00a0<\/p>\n Therefore,112_{8}=74_{10}<\/span>.<\/span><\/p>\n <\/span><\/p>\n 3. Converting Hexadecimal to Decimal<\/b><\/p>\n A hexadecimal number has the base of 16. So, if we have to convert the number into decimals, we will multiply by the decreasing power of 16.\u00a0<\/span><\/p>\n If we have the number 14_{16}<\/span><\/span>. We will convert it to decimals like this \u2013<\/span><\/p>\n 1 \\times 16^{1}+4 \\times 16^{0}<\/span><\/span><\/p>\n =16+4 <\/span><\/span><\/p>\n=20<\/span>\n Therefore,14_{16}=20_{10}<\/span>.<\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n 1. Decimals to Binary<\/b><\/p>\n When we converted binary to decimals, we multiplied by the decreasing power of 2. Here, we divide by 2 till the quotient is 0.\u00a0<\/span><\/p>\n Suppose we have a number 22_{10}<\/span>.<\/span><\/p>\n Divide 22 by 2, we get:<\/span><\/p>\n \\frac{22}{2}<\/span>= 11 Remainder \u2013 0 (most significant bit)<\/span><\/p>\n \\frac{11}{2}<\/span>= 5 remainder \u2013 1<\/span><\/p>\n \\frac{5}{2}<\/span>= 2 remainder \u2013 1<\/span><\/p>\n \\frac{2}{2}<\/span>= 1 remainder \u2013 0<\/span><\/p>\n \\frac{1}{2}<\/span> = 0 remainder – 1 (least significant bit)<\/span><\/p>\n We will write this number from the most significant bit to the least significant bit from left to right. The binary equivalent of <\/span>22_{10}=10110_{2}<\/span>.<\/span><\/p>\n <\/span><\/p>\n 2. Decimals to Octal numbers<\/b><\/p>\n In the case of converting decimals to octal numbers, we divide by 8 until we reach 0 as the quotient.<\/span><\/p>\n Consider the number 65_{10}<\/span>.<\/span><\/p>\n We will start by dividing with 8.<\/span><\/p>\n \\frac{65}{8}<\/span>= 8 Remainder \u2013 1 (most significant bit)<\/span><\/p>\n \\frac{8}{8}<\/span>= 1 Remainder \u2013 0<\/span><\/p>\n \\frac{1}{8}<\/span>= 0 remainder \u2013 1 (least significant bit)<\/span><\/p>\n Therefore, the octal number for 65_{10} \\text { is } 101_{8}<\/span>.<\/span><\/p>\n <\/span><\/p>\n 3. Decimals to Hexadecimals<\/b><\/p>\n When we convert decimals to hexadecimals we divide by 16.<\/span><\/p>\n We consider the number 110_{10}<\/span><\/span>. <\/span>We divide the number by 16.<\/span><\/p>\n \\frac{110}{6}<\/span>= 6 remainder \u2013 14<\/span><\/p>\n \\frac{6}{16}<\/span>= 0 remainder \u2013 6<\/span><\/p>\n We replace the numbers 10, 11, 12, 13, 14 with alphabets A, B, C, D, E respectively.\u00a0<\/span><\/p>\n So, we get 110_{10}=6 E_{16}<\/span>.<\/span><\/p>\n <\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}” theme_builder_area=”post_content”]<\/p>\nHOW TO READ A DECIMAL NUMBER?<\/b><\/h2>\n
CONVERTING OTHER BASES INTO DECIMAL NUMBER SYSTEM<\/b><\/h2>\n
<\/span><\/p>\nCONVERTING DECIMALS INTO OTHER BASES\u00a0<\/b><\/h2>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}” theme_builder_area=”post_content”]<\/p>\nRelated Concepts<\/h1>\n