Number systems worksheet with answers

Free printable Number systems worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0x16. What is the pattern's value N in decimal?

0x16
N =
2.Easy
place values6256F1681

Convert the hexadecimal number 0x6F8 to decimal. Find N.

0x6F8A = 10 … F = 15
N =
3.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −2 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −28 bit
U =
4.Medium
place values in two's complement1−12816413211608040201

The 8-bit pattern 1111 0000 stores a signed integer in two's complement. What is its value N in decimal?

1111 00008 bit
N =
5.Hard
605 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 605 items its own binary code of the same length. What is the smallest number of bits b needed?

605
b = bit
6.Hard
2717 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 2717 items its own binary code of the same length. What is the smallest number of bits b needed?

2717
b = bit

Answer key

  1. 1. N = 22
  2. 2. N = 1784
  3. 3. U = 254
  4. 4. N = −16
  5. 5. b = 10 bit
  6. 6. b = 12 bit

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