completed answers for number-systems

Author: TzeMingHo

number-systems/README.md

@@ -11,10 +11,10 @@ Convert the binary number 101101 to decimal:
 Answer: 2^5 + 2^3 + 2^2 + 2^0 = 32 + 8 + 4 + 1 = 45
 
 Which is larger: 1000 or 0111?
-Answer: 1000 because 1000 is 8 and 0111 is 7
+Answer: 1000 is larger because 1000 has more places
 
 Which is larger: 00100 or 01011?
-Answer: 01011 because 01011 is 11 and 00100 is 4
+Answer: 01011 is larger because it has more places
 
 What is 10101 + 01010?
 Answer: 11111
@@ -34,8 +34,8 @@ 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: 2^9 = 512
 2^8 = 256  
- 2^7 = 128  
- 2^6 = 64
+2^7 = 128  
+2^6 = 64
 2^3 = 8
 512 + 256 + 128 + 64 + 32 + 8 = 1000
 b1111101000 = 1000
@@ -44,39 +44,38 @@ 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: 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.
+If the binary number is 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*$/.test(String(binaryNumber))
-        }
+function testPowerOfTwo(binaryNumber) {
+return /^0*10*$/.test(String(binaryNumber))
+}
 
 Convert the decimal number 14 to hex.
 Answer: 10 = A, 11 = B, 12 = C, 13 = D, 14 = E
 
 Convert the decimal number 386 to hex.
-Answer: F = 15,
-386 / 15 = 25.7333
-386 - (F * 25) = 11
-So, 386 = F*25+B
+Answer: 386 - 16^2 = 130
+130 - 16 x 8 = 2
+hex: 182
 
 Convert the hex number 386 to decimal.
-Answer:
+Answer: 3 x 16^2 + 8 x 16 + 6 x 1 = 902
 
 Convert the hex number B to decimal.
-Answer:
+Answer: 11
 
 If reading the byte 0x21 as a number, what decimal number would it mean?
-Answer:
+Answer: 2 x 16 + 1 X 1 = 33
 
 If reading the byte 0x21 as an ASCII character, what character would it mean?
-Answer:
+Answer: !
 
 If reading the byte 0x21 as a greyscale colour, as described in "Approaches for Representing Colors and Images", what colour would it mean?
-Answer:
+Answer: As the byte 0x21 is 33 in decimal, which is in the range of 0 full black to 255 full white. The color is close to black.
 
 If reading the bytes 0xAA00FF as an RGB colour, as described in "Approaches for Representing Colors and Images", what colour would it mean?
-Answer:
+Answer: AA (170) means middle high red, 00 means no green, and FF (255) means full blue. The colour should be purple.
 
 If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be?
-Answer:
+Answer: 170, 0, 255