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 0xE2. What is the pattern's value N in decimal?

0xE2
N =
2.Easy
click the bits to set them012806403201608040201

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

0xAE
N =
3.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −83 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −838 bit
U =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −75 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −758 bit
U =
5.Hard
24 bits, unsigned, N = ?????????????????????????

What is the largest unsigned integer N that fits in 24 bits?

24 bit
N =
6.Hard
1648 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 1648 items its own binary code of the same length. What is the smallest number of bits b needed?

1648
b = bit

Answer key

  1. 1. N = 226
  2. 2. N = 174
  3. 3. U = 173
  4. 4. U = 181
  5. 5. N = 1.678 × 10⁷
  6. 6. b = 11 bit

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