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

0xDF
N =
2.Easy
place values012806413201618040201

Convert the binary number 0010 1000₂ to decimal. Find N.

0010 1000₂
N =
3.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −93 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −938 bit
U =
4.Medium
place values in two's complement1−12806413211618140211

The 8-bit pattern 1011 1101 stores a signed integer in two's complement. What is its value N in decimal?

1011 11018 bit
N =
5.Hard
click the bits to set them012806403201608040201

Set the bits to the 8-bit result of 0110 1100 OR 1011 1100. What is the result's value R in decimal?

0110 1100OR1011 1100
R =
6.Hard
1328 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 1328 items its own binary code of the same length. What is the smallest number of bits b needed?

1328
b = bit

Answer key

  1. 1. N = 223
  2. 2. N = 40
  3. 3. U = 163
  4. 4. N = −67
  5. 5. R = 252
  6. 6. b = 11 bit

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