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# 2.11 Conversion between binary and decimal numbers

Edited: Oct 14

A. Introduction

Turn a binary number into decimal is easy: just multiply each digit with its place value and add up. e.g. 1101 = 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8+4+1=13

B. Two ways to turn decimal into binary:

1. Divide the number by 2 until the quotient is 0, then write down all the remainder backwards.  2. Descending power of 2 and subtract:

1. Find the largest power of 2 that can fit in the decimal number x, let that be n. If x>2^n, note down 1 (from highest to lowest, i.e. left to right) otherwise note down 0.

2. x = x - 2^n

3. n=n-1 if n>=0, go back to step 1; otherwise done.

C. Try:

• Convert the following binary numbers into decimal numbers:

1011, 1101, 1111, 10001, 11001, 1100010011, 1000111011.

• Convert the following decimal numbers into binary numbers:

123, 789, 9021, 8762, -1000000, 0.5

mr.ricklu
Jul 14, 2018  wangernestrdragon
Jul 15, 2018

1)2^3+2^1+2^0=11

2)2^3+2^2+2^0=13

3)2^3+2^2+2^1+2^0=14

4)2^4+2^0=17

5)2^4+2^3+2^0=25

6)2^9+2^8+2^4+2^1+2^0=787

7)2^9+2^5+2^4+2^3+2^1+2^0=571

8)111101

9)1100010101

10)10001100111101

11)10001000111010

12)-11110100001001000000

13)0.1

tian
Jul 15, 2018

11, 13, 15, 17, 25, 787, 571

1111011, 1100010101, 10001100111101, 10001000111010, -11110100001001000000, 0.1

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