01 Number systems exercises (issue 130)

Author: Nataliia74

number-systems/README.md

@@ -5,61 +5,90 @@ 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:1110
+
+2^3 - 8 - (8<=14) - 1
+2^2 - 4 - (4<=6) - 1
+2^1 - 2 - (2<=2) - 1
+2^0 - 1 - (0<=1) - 0
 
 Convert the binary number 101101 to decimal:
-Answer:
+Answer:45
+1 - 32
+0 - 16
+1 = 8
+1 - 4
+0 - 2
+1 - 1
+
+45
 
 Which is larger: 1000 or 0111?
-Answer:
+Answer: 1000 > 0111
 
 Which is larger: 00100 or 01011?
-Answer:
+Answer: 00100 < 01011
 
 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: 15
 
 How many bits would you need in order to store the numbers between 0 and 255 inclusive?
-Answer:
+Answer: 2^8, 8 bits
 
 How many bits would you need in order to store the numbers between 0 and 3 inclusive?
-Answer:
+Answer: 2 bit
 
 How many bits would you need in order to store the numbers between 0 and 1000 inclusive?
-Answer:
+Answer: 2^10, 10 bits
 
 How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
-Answer:
+Answer: every number from range has just one of 1 bit and all the rest are zeros
 
 Convert the decimal number 14 to hex.
-Answer:
+Answer: E Took from table.
 
 Convert the decimal number 386 to hex.
-Answer:
+Answer: 182
+
+386/16 = 24 (rem 2)
+24/16 = 1 (rem 8)
+1/16 = 0 (rem 1)
 
 Convert the hex number 386 to decimal.
-Answer:
+Answer: 902
+
+3 8 6
+16^2 16^1 16^0
+3*256, 8*16, 6\*1
+768 + 128 + 6
+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: 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: 33
 
 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: maybe purpler
 
 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
+
+AA00FF
+1010 1010. 0000 0000. 1111 1111
+0000 0000 - 0
+1111 1111 - 255
+1010 1010 - 2^7+0+2^5+0+2^3+0+2^1+0 = 170