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
place valuesE256216E1

Convert the hexadecimal number 0xE2E to decimal. Find N.

0xE2EA = 10 … F = 15
N =
2.Easy
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0x1D. What is the pattern's value N in decimal?

0x1D
N =
3.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −108 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −1088 bit
U =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −89 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −898 bit
U =
5.Hard
32 bits, unsigned, N = ?????????????????????????????????

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

32 bit
N =
6.Hard
1300 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 1300 items its own binary code of the same length. What is the smallest number of bits b needed?

1300
b = bit

Answer key

  1. 1. N = 3630
  2. 2. N = 29
  3. 3. U = 148
  4. 4. U = 167
  5. 5. N = 4.295 × 10⁹
  6. 6. b = 11 bit

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