Math Alternative Assignment: Assignment 1 Dillon Yeo 6HT3 11 Jan 2018Research and Investigation:In your own words, explain what binary numbers are and how they are counted. Binary numbers are numbers from the binary numeral system (base-two number system).
They only contain the digits zero and one.(e.g. 10010010, 101010011) Invented by Gottfried Leibniz, binary numbers come from the binary system, which is used to generate binary code used by computer processors.https://en.
htmCounting binary numbers is, in a way, similar to counting in decimal. In decimal, after exhausting all the possible digits (0,1,2,3,4,5,6,7,8,9) in the ones place, the number 1 is added in the tens place and the number in the ones place starts back at 0, the first of the possible digits.(e.g. 8, 9, 10)In binary, after exhausting all the possible digits (0,1) in the ones place, the number 1 is added to the twos place and the number in the ones place starts back at 0, the first of the possible digits. This method of exhausting possible digits in the number places and using the next one keeps going on as the number being expressed increases.
Decimal—Binary0 01 12 10 (1 is added in twos place and number in ones place resets to 0)3 114 100 (possible digits in twos place exhausted, next number place used)5 1016 1107 111 8 1000 … …… …https://www.wikihow.com/Count-in-Binaryhttp://www.
mathsisfun.com/binary-number-system.html b) Illustrate binary numbers using the last two digits of your student ID (65)I can illustrate binary numbers and conversion from decimal to binary by converting 65 to a binary number.The method I am using involves dividing the decimal number being converted repeatedly by two until the number becomes zero and observing the remainder of the number every time I divide.
The remainders would read the binary equivalent of the decimal number.Process:65÷2=32 R1 32÷2=16 R016÷2=8 R0 8÷2=4 R04÷2=2 R0 2÷2=1 R01÷2=0 R1 (Divide number until quotient becomes zero)Read the values of the remainders from the bottom to the top :1000001This is the binary equivalent of 65, (1000001)2.This method works because the binary numeral system uses base two.
By dividing by two and observing the remainder, we find the digit for each number place of the binary number.c) Find the value of (101100)2 in base ten. Show working clearly.
The method I am using to convert this binary number to decimal first involves listing powers of two and matching the values in the binary number with the powers of two. I then multiply the powers of two and the binary digits before adding the products together to form the decimal equivalent of the binary number.This method is somewhat similar to reversing the method of converting decimal numbers to binary. Below is the process of conversion of (101100)2 to decimal.Process:(List down the powers of two, the number of listed powers of two being equal to the number of digits in the binary number) 32 16 8 4 2 1 1 0 1 1 0 0 (Put binary number below powers of two with each digit corresponding to one power of two above it.
) 32 16 8 4 2 1 1 0 1 1 0 0——————————– 32 8 432+8+4=44 Decimal equivalent of (101100)2 is 44( I then identify the powers of two which correspond with the binary digit ‘1’, ignoring the other powers of two corresponding with the binary digit ‘0’. Finally, I add all the identified powers of two together, the result being the decimal equivalent of (101100)2. )d) Convert (231)10 to its corresponding binary number. Show working clearly.
I am using the same method from (b) to convert (231)10 to its corresponding binary number.Process:231÷2=115 R1115÷2=57 R157÷2=28 R128÷2=14 R014÷2=7 R07÷2=3 R13÷2=1 R11÷2=0 R1 (Divide (231)10 by 2 repeatedly until it reaches zero and observe remainders from each equation)Read the values of the remainders from the bottom to the top:11100111(11100111)2 is the binary equivalent of (231)10. e) Explain how you would add (10001)2 and (100111)2 without converting to base ten.f) Explain how binary numbers are used in computers.