Question

• Explain how you convert number systems using position notation
• Convert these binary numbers to decimal
  • 1101 1100 1101 1101
  • 0100 1011 1111 0011
• Convert these decimal numbers to binary
  • 4587
  • 6311
• Convert these decimal to hexadecimal
  • 54097
  • 45923

Answer 1

1)
a)
Converting 1101 1100 1101 1101 to decimal
1101110011011101
=> 1x2^15+1x2^14+0x2^13+1x2^12+1x2^11+1x2^10+0x2^9+0x2^8+1x2^7+1x2^6+0x2^5+1x2^4+1x2^3+1x2^2+0x2^1+1x2^0
=> 1x32768+1x16384+0x8192+1x4096+1x2048+1x1024+0x512+0x256+1x128+1x64+0x32+1x16+1x8+1x4+0x2+1x1
=> 32768+16384+0+4096+2048+1024+0+0+128+64+0+16+8+4+0+1
=> 56541
Answer: 56541

b)
Converting 0100 1011 1111 0011 to decimal
0100101111110011
=> 0x2^15+1x2^14+0x2^13+0x2^12+1x2^11+0x2^10+1x2^9+1x2^8+1x2^7+1x2^6+1x2^5+1x2^4+0x2^3+0x2^2+1x2^1+1x2^0
=> 0x32768+1x16384+0x8192+0x4096+1x2048+0x1024+1x512+1x256+1x128+1x64+1x32+1x16+0x8+0x4+1x2+1x1
=> 0+16384+0+0+2048+0+512+256+128+64+32+16+0+0+2+1
=> 19443
Answer: 19443

2)
a)
Divide 4587 successively by 2 until the quotient is 0
   > 4587/2 = 2293, remainder is 1
   > 2293/2 = 1146, remainder is 1
   > 1146/2 = 573, remainder is 0
   > 573/2 = 286, remainder is 1
   > 286/2 = 143, remainder is 0
   > 143/2 = 71, remainder is 1
   > 71/2 = 35, remainder is 1
   > 35/2 = 17, remainder is 1
   > 17/2 = 8, remainder is 1
   > 8/2 = 4, remainder is 0
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1000111101011
So, 4587 of decimal is 1000111101011 in binary
Answer: 0001000111101011

b)
Divide 6311 successively by 2 until the quotient is 0
   > 6311/2 = 3155, remainder is 1
   > 3155/2 = 1577, remainder is 1
   > 1577/2 = 788, remainder is 1
   > 788/2 = 394, remainder is 0
   > 394/2 = 197, remainder is 0
   > 197/2 = 98, remainder is 1
   > 98/2 = 49, remainder is 0
   > 49/2 = 24, remainder is 1
   > 24/2 = 12, remainder is 0
   > 12/2 = 6, remainder is 0
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1100010100111
So, 6311 of decimal is 1100010100111 in binary
Answer: 0001100010100111

3)
a)
Divide 54097 successively by 16 until the quotient is 0
54097/16 = 3381, remainder is 1
3381/16 = 211, remainder is 5
211/16 = 13, remainder is 3
13/16 = 0, remainder is 13
Read remainders from the bottom to top as D351
Answer: D351

b)
Divide 45923 successively by 16 until the quotient is 0
45923/16 = 2870, remainder is 3
2870/16 = 179, remainder is 6
179/16 = 11, remainder is 3
11/16 = 0, remainder is 11
Read remainders from the bottom to top as B363
Answer: B363