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If you would like to quiz yourself on converting the numbers 0 through 255 to binary, octal, and hexadecimal (and between those bases), here’s a link to the representations of those numbers: Binary, Octal, and Hexadecimal Numbers.8086 Emulator Software Free 16 virniroz Ma8086 Emulator Software Free 16Įmulator software free download for windows 7 You may want to print out copies of these worksheets to help you with your conversions between binary and octal or hexadecimal: Remember this by recalling that 2 4 = 16, so we need four digits. Split this number into sets of three, starting with the right-most digit, then convert each set of three to its equivalent in base 8.įor hexadecimal (base 16), we need up to four digits in binary to represent each single digit.
We split each digit in base 8 to three digits in base 2, using the three digit base 2 equivalent, so 6 8 = 110 2, 1 8 = 001 2, etc. Here’s a way to remember this: 2 3 = 8, so we need three spaces. For each additional digit in base 8, we need up to three spaces to represent it in base 2.
For three digits in base 8, we need 7, 8, or 9 digits in base 2. For two digits in base 8, we need 4, 5, or 6 digits in base 2. Do you see a pattern here? For a single digit in base 8, we need up to three digits in base 2. We need four, five, or six digits in base 2 to represent these same numbers: Base 2 number In fact, the numbers 8 through 63 can be represented by two digits in base 8. Now when we get to the number 8, we need four digits in base 2 and two digits in base 8. In base eight, these numbers are represented by a single digit. This video gives a basic introduction to these conversions:įor another description, this one is more like a math lecture:įor further clarification, recall that the numbers 0 through 7 can be represented by up to three digits in base two. However, we can easily convert directly from binary to octal, and vice versa, and from binary to hexadecimal, and vice versa. If we are converting between two bases other than decimal, we typically have to convert the number to base 10 first, and then convert that number to the second base. In modern computing and digital electronics, the most commonly used bases are decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16).
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