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

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

Set the bits so the 8-bit register holds 0xF7. What is the pattern's value N in decimal?

0xF7
N =
3.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −38 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −388 bit
U =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −40 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −408 bit
U =
5.Hard
2245 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 2245 items its own binary code of the same length. What is the smallest number of bits b needed?

2245
b = bit
6.Hard
32 bits, unsigned, N = ?????????????????????????????????

What is the largest unsigned integer N that fits in 32 bits?

32 bit
N =

Answer key

  1. 1. N = 202
  2. 2. N = 247
  3. 3. U = 218
  4. 4. U = 216
  5. 5. b = 12 bit
  6. 6. N = 4.295 × 10⁹

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