设计一个简单的卷积神经网络，并用于手写数字识别的分类操作。 Conv layer1 + max pooling Conv layer2 + max pooling Full layer1+ dropout Full layer2prediction(softmax) 1）定义weights和biases； 2）加载图像数据，tensorflow.examples.tutorials.mnist； 3）建立2层卷积层+pooling层，激活函数选用tf.nn.relu； 4）建立全连接层； 5）定义优化器，误差最小化方法cross_entropy； 6）训练数据。

好的，下面是一个简单的卷积神经网络的代码，用于手写数字识别的分类操作：

import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data

# 加载MNIST数据集
mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)

# 定义输入和输出的placeholder
x = tf.placeholder(tf.float32, [None, 784])
y_true = tf.placeholder(tf.float32, [None, 10])

# 定义卷积层1
W_conv1 = tf.Variable(tf.truncated_normal([5, 5, 1, 32], stddev=0.1))
b_conv1 = tf.Variable(tf.constant(0.1, shape=[32]))
x_image = tf.reshape(x, [-1, 28, 28, 1])
h_conv1 = tf.nn.relu(tf.nn.conv2d(x_image, W_conv1, strides=[1, 1, 1, 1], padding='SAME') + b_conv1)
h_pool1 = tf.nn.max_pool(h_conv1, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')

# 定义卷积层2
W_conv2 = tf.Variable(tf.truncated_normal([5, 5, 32, 64], stddev=0.1))
b_conv2 = tf.Variable(tf.constant(0.1, shape=[64]))
h_conv2 = tf.nn.relu(tf.nn.conv2d(h_pool1, W_conv2, strides=[1, 1, 1, 1], padding='SAME') + b_conv2)
h_pool2 = tf.nn.max_pool(h_conv2, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')

# 定义全连接层1
W_fc1 = tf.Variable(tf.truncated_normal([7 * 7 * 64, 1024], stddev=0.1))
b_fc1 = tf.Variable(tf.constant(0.1, shape=[1024]))
h_pool2_flat = tf.reshape(h_pool2, [-1, 7 * 7 * 64])
h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)
keep_prob = tf.placeholder(tf.float32)
h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

# 定义全连接层2和预测输出
W_fc2 = tf.Variable(tf.truncated_normal([1024, 10], stddev=0.1))
b_fc2 = tf.Variable(tf.constant(0.1, shape=[10]))
y_pred = tf.nn.softmax(tf.matmul(h_fc1_drop, W_fc2) + b_fc2)

# 定义损失函数和优化器
cross_entropy = tf.reduce_mean(-tf.reduce_sum(y_true * tf.log(y_pred), reduction_indices=[1]))
train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)

# 定义评估模型的准确率
correct_prediction = tf.equal(tf.argmax(y_pred, 1), tf.argmax(y_true, 1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))

# 训练模型
with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    for i in range(20000):
        batch = mnist.train.next_batch(50)
        if i % 100 == 0:
            train_accuracy = accuracy.eval(feed_dict={x: batch[0], y_true: batch[1], keep_prob: 1.0})
            print("step %d, training accuracy %g" % (i, train_accuracy))
        train_step.run(feed_dict={x: batch[0], y_true: batch[1], keep_prob: 0.5})
    print("test accuracy %g" % accuracy.eval(feed_dict={x: mnist.test.images, y_true: mnist.test.labels, keep_prob: 1.0}))

这个卷积神经网络有两个卷积层和一个全连接层。第一个卷积层有32个卷积核，第二个卷积层有64个卷积核。每个卷积层后面都有一个最大池化层。在全连接层1中使用了dropout技术以防止过拟合。损失函数使用交叉熵，优化器使用Adam优化器。在训练过程中，每100步会输出一次训练准确率。最后输出测试准确率。