Converting Between Bases

Hexadecimal to Binary

Take the hexadecimal number and find the binary equivalent place values that equal that specific number. Hex to binary conversion examples (1E3)16 = (0001 1110 0011)2 (0A2B)16 = (0000 1010 0010 1011)2 (7E0C)16 = (0111 1110 0000 1100)2

Decimal to Binary

Each Decimal binary digit is encoded as binary using 4 bits (0000-1111). 7093 = (in BCD) involves the individual conversion of each number. Write out all of the place values/weights of the digits possible in binary and line them up with the decimal value. Dec: 7093 Bin: 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1 Now, what places/values would add up to equal 7093? The places that add up to 7093 become ticked with a 1 and the others, coming from the left most digit, all the way to the right most, are ticked with a 0. The result is your converted binary digit. Decimal to binary conversion examples (51)10 = (110011)2 (217)10 = (11011001)2 (8023)10 = (1111101010111)2

Hexadecimal to Decimal

Examples: 3A = 3x16^1 + A (10) = 58 (Dec) F1 = 15x16^1 + 1 = 240 + 1 = 241 (Dec) 4AB = 4x256 + A (10)x16 + B (11) = 1024 + 160 + 11 = 1195 (Dec)

Binary to Decimal

The first four digits of a binary will decide the first hexadecimal number. 1101 -> Hex (1x2^3) + (1x2^2) + (0x2^1) + (1x2^0) 8 + 4 + 1 = 13 -> Hex = D (13) (00 10)(101)(1100) 1 + 5 + 12 = Hex -> 15C

Octal to Binary

When you take any Octal number, you break it down into individual numbers and immediately reference the tables (binary three bit table). Simply convert the number to binary, as they are individually separated, then merely join them together (remove any zeroes that may be on the leftmost end, as they are irrelevant). Three binary digits for the Octal number. Example: Octal - 16 (convert to Binary) / \ 001 = 1 6 = 110 = 001110 = 1110 Bin -> Oct 001110 / \ 1 6