Intro to Programming - Decimal, Binary, Octal, and Hexadecimal conversions / Signed Integers
hexadecimal
-base 16 -has 16 digit symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
binary
-base 2 -has 2 digit symbols: 0, 1
octal
-base 8 -has 8 digit symbols: 0, 1, 2, 3, 4, 5, 6, 7
converting octal to binary
-convert each individual digit in the number to three binary digits ex. 23 2 = 010 , 3 = 011 answer: 010011
converting hex to octal
-convert hex to binary -mark in groups of 3 from right to left -translate each group ex. 7C4 011111000100 011 111 000 100 011 = 3 , 111 = 7 , 000 = 0 , 100 = 4 answer: 3704
converting octal to hex
-convert octal to binary and then binary to hex -
converting decimal to hex
-divide decimal number by 16 -keep dividing answer by 16 until you get 0 -the answer is remainders of each, from last to first ex. 1988 1988/16 = 124 remainder 4 124/16 = 7 remainder 12 = C 7/16 = 0 remainder 7 answer: 7C4
converting decimal to octal
-divide the decimal number by 8 -keep dividing the answer by 8 until you get 0 -answer is the remainders of each, from last to first ex. 1988 1988/8 = 248 remainder 4 248/8 = 31 remainder 0 31/8 = 3 remainder 7 3/8 = 0 remainder 3 answer: 3704
converting binary to hex
-mark groups of four from right to left -translate each group ex. 10101011 1010 1011 10 = A , 11 = B answer:
converting binary to octal
-mark groups of three from right to left -translate each group ex. 10101011 10 101 011 10 = 2 , 101 = 5 , 011 = 3 answer: 253
forming two's complement
-reverse each bit in the original value -add 1 to that value -the sum is answer
how to get twos complement
-write out the number in binary -invert the digits -add one to the result
decimal
base 10
two's complement
negative #'s are stored in two's complement notation
signed integers
the first bit indicates the sign. 1 = negative, 0 = positive
twos complement explanation
the two's complement of an N-bit number is defined as its complement with respect to 2N
