https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/number-systems-introduction 2023-11-15T19:12:44.061361401Z Introduction to number systems and binary The base 10 (decimal) system is the most common number system used by humans, but there are other important and useful number systems. For example, base 2, called binary system, is the basis of modern computing. We can convert between the decimal form and binary form of a number to solve different problems. video https://cdn.kastatic.org/googleusercontent/t148CvAeNinMgKJuOAWKS5UAYHXWpnTe71gf2rlM9hY-61PPWMCpdUbxTttTUmVogpP2GQoUWziD_fcNMjFEWmQ3VA Introduction to number systems and binary The base 10 (decimal) system is the most common number system used by humans, but there are other important and useful number systems. For example, base 2, called binary system, is the basis of modern computing. We can convert between the decimal form and binary form of a number to solve different problems. https://cdn.kastatic.org/ka-youtube-converted/ku4KOFQ-bB4.mp4/ku4KOFQ-bB4.mp4 600 Bases of Number Systems https://www.khanacademy.org/computing/computers-and-internet/xcae6f4a7ff015e7d:digital-information/xcae6f4a7ff015e7d:binary-numbers/a/bits-and-binary 2021-04-29T08:00:13Z Binary numbers article https://www.khanacademy.org/math/grade-8-math-snc-aligned/x4383bdbca3d6abf7:numbers-and-operations/x4383bdbca3d6abf7:bases-of-number-systems/e/binary-1 2021-07-26T21:45:22.912379873Z Binary numbers Practice binary numbers. exercise https://www.khanacademy.org/computing/computers-and-internet/xcae6f4a7ff015e7d:digital-information/xcae6f4a7ff015e7d:binary-numbers/v/the-binary-number-system 2023-07-28T19:15:55.943032354Z The binary number system Binary numbers form the basis of computing systems. Binary numbers contain only the digits 0 or 1, or bits, where each bit represents a power of two. To convert binary to decimal, multiply each bit by its corresponding power of two and add the results. Pamela Fox video https://cdn.kastatic.org/googleusercontent/0zw192LXsHphioLOEwcMMq81dSmtF8pMMwBnyQ2XlNA40D8IDZJ486e8wU-z67k6VclmeID48LbyXDPnRbrW7ZX2 The binary number system Binary numbers form the basis of computing systems. Binary numbers contain only the digits 0 or 1, or bits, where each bit represents a power of two. To convert binary to decimal, multiply each bit by its corresponding power of two and add the results. https://cdn.kastatic.org/ka-youtube-converted/sXxwr66Y79Y.mp4/sXxwr66Y79Y.mp4 345 Bases of Number Systems https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/hexadecimal-number-system 2023-11-15T19:12:44.061361401Z Hexadecimal number system The hexadecimal number system is a way of counting that uses 16 different symbols instead of just the ten we're used to. It uses the numbers 0-9 like we do, but it also uses the letters A-F to represent the numbers 10-15. This system is useful in computer science because it can represent large numbers in a shorter, more compact way. video https://cdn.kastatic.org/googleusercontent/KIba5AZQbl9H7LhUWbqGq0o9hyvrLtaYtFS1_JGZm6XM5aWqb1nQ5mKOx_-YuI52ulka7c2zj6RkRUFM-fv-oaoN Hexadecimal number system The hexadecimal number system is a way of counting that uses 16 different symbols instead of just the ten we're used to. It uses the numbers 0-9 like we do, but it also uses the letters A-F to represent the numbers 10-15. This system is useful in computer science because it can represent large numbers in a shorter, more compact way. https://cdn.kastatic.org/ka-youtube-converted/4EJay-6Bioo.mp4/4EJay-6Bioo.mp4 454 Bases of Number Systems https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/binary-to-hexadecimal 2023-11-15T19:12:44.061361401Z Converting directly from binary to hexadecimal To convert from binary to hexadecimal, we can split the binary number into groups of four digits. Each group of four binary digits can be converted into one hexadecimal digit. We can use a table or chart to figure out which hexadecimal digit matches each group of four binary digits. Once we have converted each group, we put the hexadecimal digits together to get the final answer. video https://cdn.kastatic.org/googleusercontent/LehvyVh-Z0jHaa7GZn47kyJLdmQ90KeDAORc_hv4N4h8_KQmgQNhPurwkS2hqcYPqFsQ1jIjUiRmj4yISL68pUaI Converting directly from binary to hexadecimal To convert from binary to hexadecimal, we can split the binary number into groups of four digits. Each group of four binary digits can be converted into one hexadecimal digit. We can use a table or chart to figure out which hexadecimal digit matches each group of four binary digits. Once we have converted each group, we put the hexadecimal digits together to get the final answer. https://cdn.kastatic.org/ka-youtube-converted/8T4F7WboWPQ.mp4/8T4F7WboWPQ.mp4 327 Bases of Number Systems https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/decimal-to-binary 2023-11-15T19:12:44.061361401Z Converting from decimal to binary To convert a number from decimal to binary, we need to figure out which combination of 0s and 1s will represent the number. Start by finding the largest power of 2 that fits into the number, write down a "1" to represent that power of 2, and subtract it from the number. We keep going until we reach the smallest power of 2, which is 1. video https://cdn.kastatic.org/googleusercontent/Q3vICe_YaYb8_4eUs3TciaKQn7lE6AfIR3cCvolIja-HVJmgl2wddgNDprLkIq3Fys7v8iHYPpbIQ_m6gjR5zOCj4g Converting from decimal to binary To convert a number from decimal to binary, we need to figure out which combination of 0s and 1s will represent the number. Start by finding the largest power of 2 that fits into the number, write down a "1" to represent that power of 2, and subtract it from the number. We keep going until we reach the smallest power of 2, which is 1. https://cdn.kastatic.org/ka-youtube-converted/H4BstqvgBow.mp4/H4BstqvgBow.mp4 232 Bases of Number Systems https://www.khanacademy.org/computing/computers-and-internet/xcae6f4a7ff015e7d:digital-information/xcae6f4a7ff015e7d:binary-numbers/v/decimal-system-refresher 2021-07-14T15:12:00Z Decimal system refresher Review how the decimal number system works before diving into the binary number system. The decimal number system and binary number system work the same way; the only difference is what each digit represents (0-9 versus 0/1). Pamela Fox video https://cdn.kastatic.org/googleusercontent/wD8KhyRPI7AStA49OTmoc4DYb630sC7ZiQamT5WJZ5CQlz_LvwxP9CxkNbtsrJ0zNozMz-4Ei57frPVaURQsgctx Decimal system refresher Review how the decimal number system works before diving into the binary number system. The decimal number system and binary number system work the same way; the only difference is what each digit represents (0-9 versus 0/1). https://cdn.kastatic.org/ka-youtube-converted/G4doTGQPRPw.mp4/G4doTGQPRPw.mp4 90 Bases of Number Systems https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/large-number-decimal-to-binary 2023-11-15T19:12:44.061361401Z Converting larger number from decimal to binary To convert a number from decimal to binary, we need to figure out which combination of 0s and 1s will represent the number. Start by finding the largest power of 2 that fits into the number, write down a "1" to represent that power of 2, and subtract it from the number. We keep going until we reach the smallest power of 2, which is 1. video https://cdn.kastatic.org/googleusercontent/WnjiS103eKZYSMncFjPRjxfQDOOqsNeTmZOZeZaXyulP8IrgTDtfwSReV6x8CQZ594xeQfWOEDxoE3eFoydswxUb Converting larger number from decimal to binary To convert a number from decimal to binary, we need to figure out which combination of 0s and 1s will represent the number. Start by finding the largest power of 2 that fits into the number, write down a "1" to represent that power of 2, and subtract it from the number. We keep going until we reach the smallest power of 2, which is 1. https://cdn.kastatic.org/ka-youtube-converted/bvcXEJbEzSs.mp4/bvcXEJbEzSs.mp4 252 Bases of Number Systems https://www.khanacademy.org/computing/computers-and-internet/xcae6f4a7ff015e7d:digital-information/xcae6f4a7ff015e7d:binary-numbers/v/converting-decimal-numbers-to-binary 2026-05-06T06:30:43.913440672Z Converting decimal numbers to binary Convert decimal numbers to binary using place values. Starting from the left, compare each binary place value, which is a power of two, to the decimal number. If the place value is less than or equal to the decimal number, put a 1 in that position, subtract the place value, and move to the next place. Otherwise, put a 0 and continue. Pamela Fox video https://cdn.kastatic.org/googleusercontent/9HKoFe3QoAAAcEd1hHgxrNhMRrX7JHl7eMR2PXQudmf3WhwBN_Mh-lPgXnU7UJP0fQhG1GolbOKdR-D0tpZiIbkc Converting decimal numbers to binary Convert decimal numbers to binary using place values. Starting from the left, compare each binary place value, which is a power of two, to the decimal number. If the place value is less than or equal to the decimal number, put a 1 in that position, subtract the place value, and move to the next place. Otherwise, put a 0 and continue. https://cdn.kastatic.org/ka-youtube-converted/1MGBapRPzqE.mp4/1MGBapRPzqE.mp4 311 Bases of Number Systems https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/binary-addition 2023-11-15T19:12:44.061361401Z Adding in binary When we add two numbers in binary, the key is that we can only use the digits zero and one. When we add two ones together, the result is two, but we have to write it as "10" in binary. Sometimes we have to "carry" a one over just like in regular addition. video https://cdn.kastatic.org/googleusercontent/5ScXDp4UcjbZt0uPn8-GRwfR-CL8RrInDUX14WGoUZCJjHeeAKYuXfmAhNKnNLA6qCZj0lshxljY-5KWsaz9GNY- Adding in binary When we add two numbers in binary, the key is that we can only use the digits zero and one. When we add two ones together, the result is two, but we have to write it as "10" in binary. Sometimes we have to "carry" a one over just like in regular addition. https://cdn.kastatic.org/ka-youtube-converted/RgklPQ8rbkg.mp4/RgklPQ8rbkg.mp4 168 Bases of Number Systems https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/binary-multiplication 2023-11-15T19:12:44.061361401Z Multiplying in binary To multiply numbers in base 2, we can use the same process as we would in base 10, but with only two digits: 0 and 1. Start by multiplying the rightmost digit of one number by each digit of the other number, working left. Keep track of any "carries" (when the product is 2, carry over a 1 to the next column). Finally, add up all the partial products. video https://cdn.kastatic.org/googleusercontent/UNALwM70x_YnAwWkEMY07iF7amTB-9_xx6YlbzJLQrXYjluM-49n10QAkUsuxEzjDe_bQVByHFxoz6K2ip5VjwM Multiplying in binary To multiply numbers in base 2, we can use the same process as we would in base 10, but with only two digits: 0 and 1. Start by multiplying the rightmost digit of one number by each digit of the other number, working left. Keep track of any "carries" (when the product is 2, carry over a 1 to the next column). Finally, add up all the partial products. https://cdn.kastatic.org/ka-youtube-converted/xHWKYFhhtJQ.mp4/xHWKYFhhtJQ.mp4 260 Bases of Number Systems