answering number-systems

Author: TzeMingHo

number-systems/README.md

@@ -5,43 +5,60 @@ Do not convert any binary numbers to decimal when solving a question unless the
 The goal of these exercises is for you to gain an intuition for binary numbers. Using tools to solve the problems defeats the point.
 
 Convert the decimal number 14 to binary.
-Answer:
+Answer: 1000 + 0100 + 0010 = 1110 = 8 + 4 + 2 = 14
 
 Convert the binary number 101101 to decimal:
-Answer:
+Answer: 2^5 + 2^3 + 2^2 + 2^0 = 32 + 8 + 4 + 1 = 45
 
 Which is larger: 1000 or 0111?
-Answer:
+Answer: 1000 because 1000 is 8 and 0111 is 7
 
 Which is larger: 00100 or 01011?
-Answer:
+Answer: 01011 because 01011 is 11 and 00100 is 4
 
 What is 10101 + 01010?
-Answer:
+Answer: 11111
 
 What is 10001 + 10001?
-Answer:
+Answer: 100010
 
 What's the largest number you can store with 4 bits, if you want to be able to represent the number 0?
-Answer:
+Answer: 1111
 
 How many bits would you need in order to store the numbers between 0 and 255 inclusive?
-Answer:
+Answer: 2^8 = 256. So, we need 7 bits. b0000000 = 0, and b1111111 = 255
 
 How many bits would you need in order to store the numbers between 0 and 3 inclusive?
-Answer:
+Answer: 2 bits as 00 = 0, and 11 = 3
 
 How many bits would you need in order to store the numbers between 0 and 1000 inclusive?
-Answer:
+Answer: 2^9 = 512
+2^8 = 256  
+ 2^7 = 128  
+ 2^6 = 64
+2^3 = 8
+512 + 256 + 128 + 64 + 32 + 8 = 1000
+b1111101000 = 1000
+we need 10 bits
 
 How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
-Answer:
+Answer: 1, 10, 100, 1000, 10000
+1, 2, 4, 8, 16
+If the binary starts with 1 or 1 followed by 0s, it will be a power of two.
+We can use regexp to test the binary number.
+
+        function testPowerOfTwo(binaryNumber) {
+            return /^0*10*$/.test(String(binaryNumber))
+        }
 
 Convert the decimal number 14 to hex.
-Answer:
+Answer: 10 = A, 11 = B, 12 = C, 13 = D, 14 = E
 
 Convert the decimal number 386 to hex.
-Answer:
+Answer: F = 15,
+386 / 15 = 25.7333
+386 - (F * 25) = 11
+So, 386 = F*25+B
 
 Convert the hex number 386 to decimal.
 Answer: